hikari.symmetry =============== .. py:module:: hikari.symmetry .. autoapi-nested-parse:: Module containing symmetry operations and point groups to be used by other objects. Submodules ---------- .. toctree:: :maxdepth: 1 /autoapi/hikari/symmetry/catalog/index /autoapi/hikari/symmetry/group/index /autoapi/hikari/symmetry/hall/index /autoapi/hikari/symmetry/operations/index Attributes ---------- .. autoapisummary:: hikari.symmetry.PG hikari.symmetry.SG Classes ------- .. autoapisummary:: hikari.symmetry.Operation hikari.symmetry.BoundedOperation hikari.symmetry.PointOperation hikari.symmetry.Group hikari.symmetry.HallSymbol hikari.symmetry.GroupCatalog Package Contents ---------------- .. py:class:: Operation(transformation, translation=np.array([0, 0, 0])) Class storing information about symmetry operations, with clear string representation and intuitive syntax for combining / utilising operations: "=" to compare two symmetry operations for logical equivalence, "*" to combine two symmetry operations or transform a vector, "** n" to apply symmetry operation n times, "% n" to restrict symmetry operation to n unit cells. Some of the functions may work incorrectly for rhombohedral unit cells #TODO .. py:class:: Type Bases: :py:obj:`enum.Enum` Enumerator class storing information about type of operation .. py:attribute:: rotoinversion :value: 4 .. py:attribute:: identity :value: 3 .. py:attribute:: reflection :value: 2 .. py:attribute:: rotation :value: 1 .. py:attribute:: inversion :value: 0 .. py:attribute:: rototranslation :value: -1 .. py:attribute:: transflection :value: -2 .. py:attribute:: translation :value: -3 .. py:property:: tf :type: numpy.ndarray .. py:property:: tl :type: numpy.ndarray .. py:method:: __eq__(other) .. py:method:: __mul__(other) .. py:method:: __pow__(power, modulo=None) .. py:method:: __repr__() .. py:method:: __str__() .. py:method:: __hash__() .. py:method:: from_code(code) :classmethod: Create new symmetry operation using symmetry code "x',y',z'" containing transformation of each individual coordinate from x,y,z to x',y',z'. :param code: string representing new coordinates after operation :return: Symmetry operation generated from given coordinate triplet code .. py:method:: from_matrix(matrix) :classmethod: Create new symmetry operation using augmented 4x4 transformation matrix :param matrix: augmented 4x4 matrix :return: Symmetry operation generated based on augmented matrix .. py:method:: from_pair(matrix, vector) :classmethod: Create new symmetry operation using point transformation 3x3 matrix and 3-length translation vector. Alias for standard creation method. :param matrix: 3x3 point transformation matrix :param vector: 3-length translation vector :return: Symmetry operation generated based on matrix - vector pair .. py:method:: _row_to_str(xyz, r) :staticmethod: Convert xyz: 3-el. list and r - number to single element of code triplet :param xyz: 3-element list of coordinates, e.g.: [1,-1,0] :param r: translation applied to the row :return: string representing change of coordinate .. py:method:: _project(vector, onto) :staticmethod: Return projection of np.ndarray "vector" to np.ndarray "onto" .. py:property:: code :type: str .. py:property:: matrix :type: numpy.ndarray Augmented 4 x 4 transformation matrix with float-type values .. py:property:: det :type: int Determinant of 3x3 transformation part of operation's matrix .. py:property:: typ :type: Type Crystallographic type of this symmetry operation (see `Type`) .. py:property:: name :type: str 'm', '3' or '2_1' :type: Short name of symmetry operation, e.g. .. py:property:: fold :type: int Number of times operation must be repeated to become identity, inversion or translation: n for n-fold axes, 2 for reflections, 1 for other (max 6) .. py:property:: order :type: int Number of times operation has to be repeated to become a translation, e.g.: n for all n-fold axes, 2 for other (max 6) .. py:property:: glide :type: numpy.ndarray Part of the translation vector stemming from operations' glide .. py:property:: glide_fold :type: int Number of types glide component of the operation must be repeated in order to contain only integer values, e.g.: 3 for "6_2", 4 for "d" .. py:property:: origin :type: numpy.ndarray Selected point that remains on the symmetry element after operation Loosely based on solving https://math.stackexchange.com/q/1054481/. .. py:property:: reciprocal :type: PointOperation Relevant symmetry operation in its respective reciprocal space .. py:property:: trace :type: int Trace of 3x3 transformation part of operation's matrix .. py:property:: translational :type: bool True if operation has any glide component, False otherwise .. py:property:: invariants :type: list[numpy.ndarray] List of directions not affected by this symmetry operation .. py:property:: orientation :type: Union[numpy.ndarray, None] Direction of symmetry element (if it can be defined) else None .. py:property:: sense :type: str "+" or "-", the "sense" of rotation, as given in ITC A, 11.1.2 .. py:property:: _hm_span .. py:property:: _hm_glide .. py:property:: hm_symbol :type: str .. py:property:: bounded :type: BoundedOperation Instance of self that always collapses down to Coset representative .. py:property:: unbounded :type: Operation Instance of self that can express translations beyond the unit cube .. py:property:: is_bounded :type: bool True if self is a coset representatives i.e. 0 <= tl < 1 element-wise .. py:method:: at(point) Transform operation as little as possible so that its symmetry element contains "point". To be used after "into" if used together. Based on "ITC 5.2.1. Transformations". :param point: Target coordinates of point which should lie in element :return: New symmetry operation which contains "point" in its element .. py:method:: into(direction, hexagonal = False) Rotate operation so that its orientation changes to "direction", while preserving fractional glide. To be used before respective "at" method. Will most likely not work for unimplemented rhombohedral unit cells. :param direction: Target orientation for element of symmetry operation :param hexagonal: True if operation is defined in hexagonal coordinates :return: New symmetry operation whose orientation is "direction" .. py:method:: transform(other) Transform a column containing rows of coordinate points :param other: A vertical numpy array of coordinate triplets kept in rows :return: Same-shaped array of coordinate triplets transformed by self .. py:method:: extincts(hkl) Return boolean array with truth whenever reflection should be extinct :param hkl: An array containing one hkl or multiple hkls in columns :return: array of booleans, where extinct reflections are marked as True .. py:method:: distance_to_point(point) .. py:class:: BoundedOperation(transformation, translation=np.array([0, 0, 0])) Bases: :py:obj:`Operation` A subclass of `Operation` where all three elements of the translation vector are bounded between 0 (inclusive) and 1 (exclusive). This class is suitable for handling coset representatives of space groups, since upon binding operations related by unit translation become equivalent. .. py:property:: tl :type: numpy.ndarray .. py:class:: PointOperation(transformation, translation=np.array([0, 0, 0])) Bases: :py:obj:`BoundedOperation` A subclass of `BoundedOperation`, asserts translation vector = [0,0,0] .. py:property:: tl :type: numpy.ndarray .. py:class:: Group(*generators) Base immutable class containing information about symmetry groups. It stores information for point and space groups and, among others, allows for iteration over its `hikari.symmetry.BoundedOperation` elements. .. py:class:: System Bases: :py:obj:`enum.Enum` Enumerator class with information about associated crystal system .. py:attribute:: triclinic :value: 0 .. py:attribute:: monoclinic :value: 1 .. py:attribute:: orthorhombic :value: 2 .. py:attribute:: trigonal :value: 3 .. py:attribute:: tetragonal :value: 4 .. py:attribute:: cubic :value: 5 .. py:attribute:: hexagonal :value: 6 .. py:property:: directions :type: list[numpy.ndarray] .. py:attribute:: BRAVAIS_PRIORITY_RULES :value: 'A+B+C=F>R>I>C>B>A>H>P' .. py:attribute:: AXIS_PRIORITY_RULES :value: '6>61>62>63>64>65>-6>4>41>42>43>-4>-3>3>31>32>2>21' .. py:attribute:: PLANE_PRIORITY_RULES :value: 'm>a+b=e>a+c=e>b+c=e>a>b>c>n>d' .. py:attribute:: __generators :value: [] .. py:attribute:: __operations .. py:attribute:: name .. py:attribute:: number :value: 0 .. py:method:: from_generators_operations(generators, operations) :classmethod: Generate group using already complete list of generators and operators. Does not check if `operations` are correct or complete for efficiency! :param generators: A complete list of group generators :param operations: A complete list of group operations :return: Symmetry group with given generators and operators. .. py:method:: from_hall_symbol(hall_symbol) :classmethod: .. py:method:: __eq__(other) .. py:method:: __lt__(other) .. py:method:: __gt__(other) .. py:method:: __le__(other) .. py:method:: __ge__(other) .. py:method:: __repr__() .. py:method:: __str__() .. py:method:: __hash__() .. py:property:: auto_generated_name :type: str Name of the group generated automatically. Use only as approx. .. py:property:: centering_symbol :type: str .. py:property:: generators :type: list[hikari.symmetry.operations.BoundedOperation] .. py:property:: operations :type: list[hikari.symmetry.operations.BoundedOperation] .. py:property:: order :type: int .. py:property:: is_centrosymmetric :type: bool True if group has centre of symmetry; False otherwise. .. py:property:: is_enantiogenic :type: bool True if determinant of any operation in group is negative. .. py:property:: is_sohncke :type: bool True if determinant of all operations in group are positive. .. py:property:: is_achiral .. py:property:: is_chiral .. py:property:: is_symmorphic :type: bool .. py:property:: is_polar :type: bool .. py:property:: system :type: System Predicted crystal system associated with this group .. py:method:: lauefy() :return: New PointGroup with centre of symmetry added to generators. :rtype: Group .. py:method:: reciprocate() .. py:method:: transform(m) Transform the group using 4x4 matrix. For reference, see `bilbao resources `_ or `IUCr pamphlet no. 22 `_. :example: >>> import numpy >>> from hikari.symmetry import SG >>> matrix = numpy.array([(1,0,1,0),(0,1,0,0),(-1,0,0,0),(0,0,0,1)]) >>> SG['P21/c'].transform(matrix).auto_generated_name P 21/n :param m: A 4x4 array containing information about new base and origin. :type m: np.ndarray :return: Group with new, transformed basis and origin. :rtype: Group .. py:class:: HallSymbol(hall_symbol) Parse, interpret, and convert Hall symbol to `hikari.symmetry.Group` .. py:exception:: HallSymbolException Bases: :py:obj:`Exception` Exception raised when group can't be generated from the symbol .. py:attribute:: REGEX This is a regex which matches every possible lowercase Hall symbol for classical 3D space groups. It matches up to 17 groups in total as follows: 1. Centrosymmetry: `[-]?` 2. Lattice symbol: `[pabcirstf]` (required) 3. Generator 1 inversion component: `[-]?` 4. Generator 1 rotation fold: `\d` (required) 5. Generator 1 rotation direction: `[*xyz]?` 6. Generator 1 translation components: `[12345abcnuvwd]*` 7. Generator 2 inversion component: `[-]?` 8. Generator 2 rotation fold: `\d` 9. Generator 2 rotation direction: `['"xyz]?` 10. Generator 2 translation components: `[12345abcnuvwd]*` 11. Generator 3 inversion component: `[-]?` 12. Generator 3 rotation fold: `\d` 13. Generator 3 translation components: `[12345abcnuvwd]*` 14. Generator 4 rotation fold: `\d` 15. Generator 4 translation components: `[12345abcnuvwd]*` 16. Origin shift constituent 1 expressed as count of 1/12 shifts: `\d` 17. Origin shift constituent 2 expressed as count of 1/12 shifts: `\d` 18. Origin shift constituent 3 expressed as count of 1/12 shifts: `\d` .. py:attribute:: DIRECTION_SYMBOLS :value: ("'", '"', '*') .. py:attribute:: TRANSLATION_SYMBOLS :value: '12345abcnuvwd' .. py:attribute:: LATTICE_GENERATORS .. py:attribute:: UNIVERSAL_MATRICES .. py:attribute:: PRINCIPAL_ROTATIONS .. py:attribute:: FACE_X_DIAGONAL_ROTATIONS .. py:attribute:: FACE_Y_DIAGONAL_ROTATIONS .. py:attribute:: FACE_Z_DIAGONAL_ROTATIONS .. py:attribute:: BODY_DIAGONAL_ROTATIONS .. py:attribute:: STATIC_TRANSLATIONS .. py:attribute:: DYNAMIC_TRANSLATIONS .. py:property:: symbol :type: str .. py:property:: elements :type: Union[None, Match] Return `self.symbol` elements indexed as in `self.HALL_REGEX` doc .. py:property:: generators :type: List[hikari.symmetry.operations.BoundedOperation] .. py:class:: GroupCatalog(table) Manage generating and mappings of point and space groups. Relies on a built-in pandas DataFrame `table` to store all the information. Individual columns are named & generated based on `GroupCatalogKey` data. For Some notes on the uniqueness of columns pairwise for accessing: - Column `Hall` has 3 groups appear twice due to inconsistency of HM names: `c_2_2_-1ac`, `a_2_2_-1ab`, and `b_2_2_-1ab`. - There are no overlaps between `HM` and `Hall` column names - There are no overlaps between `HM_short` and `Hall` column names - There are no overlaps between `HM_simple` and `Hall` column names - There are no overlaps between `HM_simple` and `HM` column names - There are 345 overlaps between `HM_simple` and `HM_short` column names .. py:attribute:: KEYS :type: list[GroupCatalogKey] .. py:attribute:: REST_COL_FORMAT .. py:attribute:: table :type: pandas.DataFrame .. py:method:: __eq__(other) .. py:method:: __len__() .. py:method:: from_json(text) :classmethod: Load from a json-formatted string .. py:method:: to_json(json_path) .. py:method:: to_rest_table(txt_path) Generate a .txt file with ReST table containing `GroupCatalog` elements. .. py:property:: accessors :type: list[GroupCatalogKey] Lists `cls.KEYS whose accessor priority is not 0 in decreasing order .. py:property:: standard :type: GroupCatalog A subset of current catalog with standard-setting groups only .. py:method:: keys() .. py:method:: values() .. py:method:: items() .. py:method:: _get_by_key(key) Iterate over accessors; whenever key is in accessor, return matching group .. py:method:: _get_by_kwargs(**kwargs) Return the first group that matches all queries specified in kwargs .. py:method:: get(key = None, **kwargs) Get first `Group` matching provided anonymous&known accessors or None .. py:method:: __getitem__(item) Get first `Group` matching provided anonymous accessor or raise .. py:data:: PG Since hikari's groups do not carry information about lattice translations, hikari does not differentiate between point groups and space groups. As a result, all groups are instances of the same class `Group`, and are stored in almost identical `GroupCatalog`s. This pre-defined `GroupCatalog` `PG` holds and provides access to all pre-defined point groups available in hikari. The point groups are named and generated based on a wsv file in resources. Individual groups can be accessed in two different ways: - using a dict-like anonymous accessor: `PG[32]`, `PG['m-3m']`; - using `get()` method: `PG.get(number=32)`, `PG.get(HM_short='m-3m')`; The `get()` method can use a combination of various keywords to unambiguously localize the correct space group. The following keyword arguments can be used: - `n_c` - unique "number:setting" string identifying each group - `number` - index of the point group as given in ICT A (integer)\* - `setting` - arbitrary string declaring group setting - `HM` - Full underscore-delimited Hermann-Mauguin symbol\* - `HM_short` - Hermann-Mauguin symbol with underscores removed\* - `HM_simple` - Short Hermann-Mauguin symbol without setting information\* - `HM_numbered` - "number: Short Hermann-Mauguin symbol" string - `Hall` - Full Hall symbol\* - `standard` - True for groups in standard setting only The keywords marked with "*" are called "accessors" and can be used to `get` the group using bracket notation `get[accessor]`. If `get` finds ambiguity, If `get` finds ambiguity, for example `PG['2/m']` matches all settings of point group #5: `1_2/m_1` (std), `1_1_2/m`, and `2/m_1_1`, the user is warned and the first group in std setting, if possible, is returned. The following table lists all possible values of selected point `Group` keywords. Please mind that in the raw docstring all `\` should be ignored. +---------+------------------+------------------+-------------+-------------+ | n_c | Hall | HM | HM_short | HM_simple | +---------+------------------+------------------+-------------+-------------+ | 1 | 1 | 1 | 1 | 1 | +---------+------------------+------------------+-------------+-------------+ | 2 | -1 | -1 | -1 | -1 | +---------+------------------+------------------+-------------+-------------+ | 3:b | 2y | 1_2_1 | 121 | 2 | +---------+------------------+------------------+-------------+-------------+ | 3:c | 2 | 1_1_2 | 112 | 2 | +---------+------------------+------------------+-------------+-------------+ | 3:a | 2x | 2_1_1 | 211 | 2 | +---------+------------------+------------------+-------------+-------------+ | 4:b | -2y | 1_m_1 | 1m1 | m | +---------+------------------+------------------+-------------+-------------+ | 4:c | -2 | 1_1_m | 11m | m | +---------+------------------+------------------+-------------+-------------+ | 4:a | -2x | m_1_1 | m11 | m | +---------+------------------+------------------+-------------+-------------+ | 5:b | -2y | 1_2/m_1 | 12/m1 | 2/m | +---------+------------------+------------------+-------------+-------------+ | 5:c | -2 | 1_1_2/m | 112/m | 2/m | +---------+------------------+------------------+-------------+-------------+ | 5:a | -2x | 2/m_1_1 | 2/m11 | 2/m | +---------+------------------+------------------+-------------+-------------+ | 6 | 2_2 | 2_2_2 | 222 | 222 | +---------+------------------+------------------+-------------+-------------+ | 7 | 2\_-2 | m_m_2 | mm2 | mm2 | +---------+------------------+------------------+-------------+-------------+ | 8 | -2_2 | m_m_m | mmm | mmm | +---------+------------------+------------------+-------------+-------------+ | 9 | 4 | 4 | 4 | 4 | +---------+------------------+------------------+-------------+-------------+ | 10 | -4 | -4 | -4 | -4 | +---------+------------------+------------------+-------------+-------------+ | 11 | -4 | 4/m | 4/m | 4/m | +---------+------------------+------------------+-------------+-------------+ | 12 | 4_2 | 4_2_2 | 422 | 422 | +---------+------------------+------------------+-------------+-------------+ | 13 | 4\_-2 | 4_m_m | 4mm | 4mm | +---------+------------------+------------------+-------------+-------------+ | 14 | -4_2 | -4_2_m | -42m | -42m | +---------+------------------+------------------+-------------+-------------+ | 15 | -4_2 | 4/m_m_m | 4/mmm | 4/mmm | +---------+------------------+------------------+-------------+-------------+ | 16 | 3 | 3 | 3 | 3 | +---------+------------------+------------------+-------------+-------------+ | 17 | -3 | -3 | -3 | -3 | +---------+------------------+------------------+-------------+-------------+ | 18 | 3_2 | 3_1_2 | 312 | 312 | +---------+------------------+------------------+-------------+-------------+ | 19 | 3\_-2" | 3_m_1 | 3m1 | 3m1 | +---------+------------------+------------------+-------------+-------------+ | 20 | -3_2 | -3_1_m | -31m | -31m | +---------+------------------+------------------+-------------+-------------+ | 21 | 6 | 6 | 6 | 6 | +---------+------------------+------------------+-------------+-------------+ | 22 | -6 | -6 | -6 | -6 | +---------+------------------+------------------+-------------+-------------+ | 23 | -6 | 6/m | 6/m | 6/m | +---------+------------------+------------------+-------------+-------------+ | 24 | 6_2 | 6_2_2 | 622 | 622 | +---------+------------------+------------------+-------------+-------------+ | 25 | 6\_-2 | 6_m_m | 6mm | 6mm | +---------+------------------+------------------+-------------+-------------+ | 26 | -6_2 | -6_m_2 | -6m2 | -6m2 | +---------+------------------+------------------+-------------+-------------+ | 27 | -6_2 | 6/m_m_m | 6/mmm | 6/mmm | +---------+------------------+------------------+-------------+-------------+ | 28 | 2_2_3 | 2_3 | 23 | 23 | +---------+------------------+------------------+-------------+-------------+ | 29 | -2_2_3 | m\_-3 | m-3 | m-3 | +---------+------------------+------------------+-------------+-------------+ | 30 | 4_2_3 | 4_3_2 | 432 | 432 | +---------+------------------+------------------+-------------+-------------+ | 31 | -4_2_3 | -4_3_m | -43m | -43m | +---------+------------------+------------------+-------------+-------------+ | 32 | -4_2_3 | m\_-3_m | m-3m | m-3m | +---------+------------------+------------------+-------------+-------------+ .. py:data:: SG Since hikari's groups do not carry information about lattice translations, hikari does not differentiate between point groups and space groups. As a result, all groups are instances of the same class `Group`, and are stored in almost identical `GroupCatalog`s. This pre-defined `SpaceGroupCatalog` `SG` holds and provides access to all pre-defined space groups available in hikari. The space groups are named and generated based on a wsv file in resources. Individual groups can be accessed in two different ways: - using a dict-like anonymous accessor: `PG[62]`, `PG['Pnma']`; - using `get()` method: `PG.get(number=62)`, `PG.get(HM_short='Pnma')`; The `get()` method can use a combination of various keywords to unambiguously localize the correct space group. The following keyword arguments can be used: - `n_c` - unique "number:setting" string identifying each group - `number` - index of the point group as given in ICT A (integer)\* - `setting` - arbitrary string declaring group setting - `HM` - Full underscore-delimited Hermann-Mauguin symbol\* - `HM_short` - Hermann-Mauguin symbol with underscores removed\* - `HM_simple` - Short Hermann-Mauguin symbol without setting information\* - `HM_numbered` - "number: Short Hermann-Mauguin symbol" string - `Hall` - Full Hall symbol\* - `standard` - True for groups in standard setting only The keywords marked with "*" are called "accessors" and can be used to `get` the group using bracket notation `get[accessor]`. If `get` finds ambiguity, for example `SG['P2/m']` matches all settings of space group #10: `P_1_2/m_1` (std), `P_1_1_2/m`, and `P_2/m_1_1`, the user is warned and the first group in std setting, if possible, is returned. The following table lists all possible values of selected space `Group` keywords. Please mind that in the raw docstring all `\` should be ignored. +---------+-----------------+-----------------+--------------+--------------+ | n_c | Hall | HM | HM_short | HM_simple | +---------+-----------------+-----------------+--------------+--------------+ | 1 | p_1 | P_1 | P1 | P1 | +---------+-----------------+-----------------+--------------+--------------+ | 2 | -p_1 | P\_-1 | P-1 | P-1 | +---------+-----------------+-----------------+--------------+--------------+ | 3:b | p_2y | P_1_2_1 | P121 | P2 | +---------+-----------------+-----------------+--------------+--------------+ | 3:c | p_2 | P_1_1_2 | P112 | P2 | +---------+-----------------+-----------------+--------------+--------------+ | 3:a | p_2x | P_2_1_1 | P211 | P2 | +---------+-----------------+-----------------+--------------+--------------+ | 4:b | p_2yb | P_1_21_1 | P1211 | P21 | +---------+-----------------+-----------------+--------------+--------------+ | 4:c | p_2c | P_1_1_21 | P1121 | P21 | +---------+-----------------+-----------------+--------------+--------------+ | 4:a | p_2xa | P_21_1_1 | P2111 | P21 | +---------+-----------------+-----------------+--------------+--------------+ | 5:b1 | c_2y | C_1_2_1 | C121 | C2 | +---------+-----------------+-----------------+--------------+--------------+ | 5:b2 | a_2y | A_1_2_1 | A121 | A2 | +---------+-----------------+-----------------+--------------+--------------+ | 5:b3 | i_2y | I_1_2_1 | I121 | I2 | +---------+-----------------+-----------------+--------------+--------------+ | 5:c1 | a_2 | A_1_1_2 | A112 | A2 | +---------+-----------------+-----------------+--------------+--------------+ | 5:c2 | b_2 | B_1_1_2 | B112 | B2 | +---------+-----------------+-----------------+--------------+--------------+ | 5:c3 | i_2 | I_1_1_2 | I112 | I2 | +---------+-----------------+-----------------+--------------+--------------+ | 5:a1 | b_2x | B_2_1_1 | B211 | B2 | +---------+-----------------+-----------------+--------------+--------------+ | 5:a2 | c_2x | C_2_1_1 | C211 | C2 | +---------+-----------------+-----------------+--------------+--------------+ | 5:a3 | i_2x | I_2_1_1 | I211 | I2 | +---------+-----------------+-----------------+--------------+--------------+ | 6:b | p\_-2y | P_1_m_1 | P1m1 | Pm | +---------+-----------------+-----------------+--------------+--------------+ | 6:c | p\_-2 | P_1_1_m | P11m | Pm | +---------+-----------------+-----------------+--------------+--------------+ | 6:a | p\_-2x | P_m_1_1 | Pm11 | Pm | +---------+-----------------+-----------------+--------------+--------------+ | 7:b1 | p\_-2yc | P_1_c_1 | P1c1 | Pc | +---------+-----------------+-----------------+--------------+--------------+ | 7:b2 | p\_-2yac | P_1_n_1 | P1n1 | Pn | +---------+-----------------+-----------------+--------------+--------------+ | 7:b3 | p\_-2ya | P_1_a_1 | P1a1 | Pa | +---------+-----------------+-----------------+--------------+--------------+ | 7:c1 | p\_-2a | P_1_1_a | P11a | Pa | +---------+-----------------+-----------------+--------------+--------------+ | 7:c2 | p\_-2ab | P_1_1_n | P11n | Pn | +---------+-----------------+-----------------+--------------+--------------+ | 7:c3 | p\_-2b | P_1_1_b | P11b | Pb | +---------+-----------------+-----------------+--------------+--------------+ | 7:a1 | p\_-2xb | P_b_1_1 | Pb11 | Pb | +---------+-----------------+-----------------+--------------+--------------+ | 7:a2 | p\_-2xbc | P_n_1_1 | Pn11 | Pn | +---------+-----------------+-----------------+--------------+--------------+ | 7:a3 | p\_-2xc | P_c_1_1 | Pc11 | Pc | +---------+-----------------+-----------------+--------------+--------------+ | 8:b1 | c\_-2y | C_1_m_1 | C1m1 | Cm | +---------+-----------------+-----------------+--------------+--------------+ | 8:b2 | a\_-2y | A_1_m_1 | A1m1 | Am | +---------+-----------------+-----------------+--------------+--------------+ | 8:b3 | i\_-2y | I_1_m_1 | I1m1 | Im | +---------+-----------------+-----------------+--------------+--------------+ | 8:c1 | a\_-2 | A_1_1_m | A11m | Am | +---------+-----------------+-----------------+--------------+--------------+ | 8:c2 | b\_-2 | B_1_1_m | B11m | Bm | +---------+-----------------+-----------------+--------------+--------------+ | 8:c3 | i\_-2 | I_1_1_m | I11m | Im | +---------+-----------------+-----------------+--------------+--------------+ | 8:a1 | b\_-2x | B_m_1_1 | Bm11 | Bm | +---------+-----------------+-----------------+--------------+--------------+ | 8:a2 | c\_-2x | C_m_1_1 | Cm11 | Cm | +---------+-----------------+-----------------+--------------+--------------+ | 8:a3 | i\_-2x | I_m_1_1 | Im11 | Im | +---------+-----------------+-----------------+--------------+--------------+ | 9:b1 | c\_-2yc | C_1_c_1 | C1c1 | Cc | +---------+-----------------+-----------------+--------------+--------------+ | 9:b2 | a\_-2yab | A_1_n_1 | A1n1 | An | +---------+-----------------+-----------------+--------------+--------------+ | 9:b3 | i\_-2ya | I_1_a_1 | I1a1 | Ia | +---------+-----------------+-----------------+--------------+--------------+ | 9:-b1 | a\_-2ya | A_1_a_1 | A1a1 | Aa | +---------+-----------------+-----------------+--------------+--------------+ | 9:-b2 | c\_-2yac | C_1_n_1 | C1n1 | Cn | +---------+-----------------+-----------------+--------------+--------------+ | 9:-b3 | i\_-2yc | I_1_c_1 | I1c1 | Ic | +---------+-----------------+-----------------+--------------+--------------+ | 9:c1 | a\_-2a | A_1_1_a | A11a | Aa | +---------+-----------------+-----------------+--------------+--------------+ | 9:c2 | b\_-2ab | B_1_1_n | B11n | Bn | +---------+-----------------+-----------------+--------------+--------------+ | 9:c3 | i\_-2b | I_1_1_b | I11b | Ib | +---------+-----------------+-----------------+--------------+--------------+ | 9:-c1 | b\_-2b | B_1_1_b | B11b | Bb | +---------+-----------------+-----------------+--------------+--------------+ | 9:-c2 | a\_-2ab | A_1_1_n | A11n | An | +---------+-----------------+-----------------+--------------+--------------+ | 9:-c3 | i\_-2a | I_1_1_a | I11a | Ia | +---------+-----------------+-----------------+--------------+--------------+ | 9:a1 | b\_-2xb | B_b_1_1 | Bb11 | Bb | +---------+-----------------+-----------------+--------------+--------------+ | 9:a2 | c\_-2xac | C_n_1_1 | Cn11 | Cn | +---------+-----------------+-----------------+--------------+--------------+ | 9:a3 | i\_-2xc | I_c_1_1 | Ic11 | Ic | +---------+-----------------+-----------------+--------------+--------------+ | 9:-a1 | c\_-2xc | C_c_1_1 | Cc11 | Cc | +---------+-----------------+-----------------+--------------+--------------+ | 9:-a2 | b\_-2xab | B_n_1_1 | Bn11 | Bn | +---------+-----------------+-----------------+--------------+--------------+ | 9:-a3 | i\_-2xb | I_b_1_1 | Ib11 | Ib | +---------+-----------------+-----------------+--------------+--------------+ | 10:b | -p_2y | P_1_2/m_1 | P12/m1 | P2/m | +---------+-----------------+-----------------+--------------+--------------+ | 10:c | -p_2 | P_1_1_2/m | P112/m | P2/m | +---------+-----------------+-----------------+--------------+--------------+ | 10:a | -p_2x | P_2/m_1_1 | P2/m11 | P2/m | +---------+-----------------+-----------------+--------------+--------------+ | 11:b | -p_2yb | P_1_21/m_1 | P121/m1 | P21/m | +---------+-----------------+-----------------+--------------+--------------+ | 11:c | -p_2c | P_1_1_21/m | P1121/m | P21/m | +---------+-----------------+-----------------+--------------+--------------+ | 11:a | -p_2xa | P_21/m_1_1 | P21/m11 | P21/m | +---------+-----------------+-----------------+--------------+--------------+ | 12:b1 | -c_2y | C_1_2/m_1 | C12/m1 | C2/m | +---------+-----------------+-----------------+--------------+--------------+ | 12:b2 | -a_2y | A_1_2/m_1 | A12/m1 | A2/m | +---------+-----------------+-----------------+--------------+--------------+ | 12:b3 | -i_2y | I_1_2/m_1 | I12/m1 | I2/m | +---------+-----------------+-----------------+--------------+--------------+ | 12:c1 | -a_2 | A_1_1_2/m | A112/m | A2/m | +---------+-----------------+-----------------+--------------+--------------+ | 12:c2 | -b_2 | B_1_1_2/m | B112/m | B2/m | +---------+-----------------+-----------------+--------------+--------------+ | 12:c3 | -i_2 | I_1_1_2/m | I112/m | I2/m | +---------+-----------------+-----------------+--------------+--------------+ | 12:a1 | -b_2x | B_2/m_1_1 | B2/m11 | B2/m | +---------+-----------------+-----------------+--------------+--------------+ | 12:a2 | -c_2x | C_2/m_1_1 | C2/m11 | C2/m | +---------+-----------------+-----------------+--------------+--------------+ | 12:a3 | -i_2x | I_2/m_1_1 | I2/m11 | I2/m | +---------+-----------------+-----------------+--------------+--------------+ | 13:b1 | -p_2yc | P_1_2/c_1 | P12/c1 | P2/c | +---------+-----------------+-----------------+--------------+--------------+ | 13:b2 | -p_2yac | P_1_2/n_1 | P12/n1 | P2/n | +---------+-----------------+-----------------+--------------+--------------+ | 13:b3 | -p_2ya | P_1_2/a_1 | P12/a1 | P2/a | +---------+-----------------+-----------------+--------------+--------------+ | 13:c1 | -p_2a | P_1_1_2/a | P112/a | P2/a | +---------+-----------------+-----------------+--------------+--------------+ | 13:c2 | -p_2ab | P_1_1_2/n | P112/n | P2/n | +---------+-----------------+-----------------+--------------+--------------+ | 13:c3 | -p_2b | P_1_1_2/b | P112/b | P2/b | +---------+-----------------+-----------------+--------------+--------------+ | 13:a1 | -p_2xb | P_2/b_1_1 | P2/b11 | P2/b | +---------+-----------------+-----------------+--------------+--------------+ | 13:a2 | -p_2xbc | P_2/n_1_1 | P2/n11 | P2/n | +---------+-----------------+-----------------+--------------+--------------+ | 13:a3 | -p_2xc | P_2/c_1_1 | P2/c11 | P2/c | +---------+-----------------+-----------------+--------------+--------------+ | 14:b1 | -p_2ybc | P_1_21/c_1 | P121/c1 | P21/c | +---------+-----------------+-----------------+--------------+--------------+ | 14:b2 | -p_2yn | P_1_21/n_1 | P121/n1 | P21/n | +---------+-----------------+-----------------+--------------+--------------+ | 14:b3 | -p_2yab | P_1_21/a_1 | P121/a1 | P21/a | +---------+-----------------+-----------------+--------------+--------------+ | 14:c1 | -p_2ac | P_1_1_21/a | P1121/a | P21/a | +---------+-----------------+-----------------+--------------+--------------+ | 14:c2 | -p_2n | P_1_1_21/n | P1121/n | P21/n | +---------+-----------------+-----------------+--------------+--------------+ | 14:c3 | -p_2bc | P_1_1_21/b | P1121/b | P21/b | +---------+-----------------+-----------------+--------------+--------------+ | 14:a1 | -p_2xab | P_21/b_1_1 | P21/b11 | P21/b | +---------+-----------------+-----------------+--------------+--------------+ | 14:a2 | -p_2xn | P_21/n_1_1 | P21/n11 | P21/n | +---------+-----------------+-----------------+--------------+--------------+ | 14:a3 | -p_2xac | P_21/c_1_1 | P21/c11 | P21/c | +---------+-----------------+-----------------+--------------+--------------+ | 15:b1 | -c_2yc | C_1_2/c_1 | C12/c1 | C2/c | +---------+-----------------+-----------------+--------------+--------------+ | 15:b2 | -a_2yab | A_1_2/n_1 | A12/n1 | A2/n | +---------+-----------------+-----------------+--------------+--------------+ | 15:b3 | -i_2ya | I_1_2/a_1 | I12/a1 | I2/a | +---------+-----------------+-----------------+--------------+--------------+ | 15:-b1 | -a_2ya | A_1_2/a_1 | A12/a1 | A2/a | +---------+-----------------+-----------------+--------------+--------------+ | 15:-b2 | -c_2yac | C_1_2/n_1 | C12/n1 | C2/n | +---------+-----------------+-----------------+--------------+--------------+ | 15:-b3 | -i_2yc | I_1_2/c_1 | I12/c1 | I2/c | +---------+-----------------+-----------------+--------------+--------------+ | 15:c1 | -a_2a | A_1_1_2/a | A112/a | A2/a | +---------+-----------------+-----------------+--------------+--------------+ | 15:c2 | -b_2ab | B_1_1_2/n | B112/n | B2/n | +---------+-----------------+-----------------+--------------+--------------+ | 15:c3 | -i_2b | I_1_1_2/b | I112/b | I2/b | +---------+-----------------+-----------------+--------------+--------------+ | 15:-c1 | -b_2b | B_1_1_2/b | B112/b | B2/b | +---------+-----------------+-----------------+--------------+--------------+ | 15:-c2 | -a_2ab | A_1_1_2/n | A112/n | A2/n | +---------+-----------------+-----------------+--------------+--------------+ | 15:-c3 | -i_2a | I_1_1_2/a | I112/a | I2/a | +---------+-----------------+-----------------+--------------+--------------+ | 15:a1 | -b_2xb | B_2/b_1_1 | B2/b11 | B2/b | +---------+-----------------+-----------------+--------------+--------------+ | 15:a2 | -c_2xac | C_2/n_1_1 | C2/n11 | C2/n | +---------+-----------------+-----------------+--------------+--------------+ | 15:a3 | -i_2xc | I_2/c_1_1 | I2/c11 | I2/c | +---------+-----------------+-----------------+--------------+--------------+ | 15:-a1 | -c_2xc | C_2/c_1_1 | C2/c11 | C2/c | +---------+-----------------+-----------------+--------------+--------------+ | 15:-a2 | -b_2xab | B_2/n_1_1 | B2/n11 | B2/n | +---------+-----------------+-----------------+--------------+--------------+ | 15:-a3 | -i_2xb | I_2/b_1_1 | I2/b11 | I2/b | +---------+-----------------+-----------------+--------------+--------------+ | 16 | p_2_2 | P_2_2_2 | P222 | P222 | +---------+-----------------+-----------------+--------------+--------------+ | 17 | p_2c_2 | P_2_2_21 | P2221 | P2221 | +---------+-----------------+-----------------+--------------+--------------+ | 17:cab | p_2a_2a | P_21_2_2 | P2122 | P2122 | +---------+-----------------+-----------------+--------------+--------------+ | 17:bca | p_2_2b | P_2_21_2 | P2212 | P2212 | +---------+-----------------+-----------------+--------------+--------------+ | 18 | p_2_2ab | P_21_21_2 | P21212 | P21212 | +---------+-----------------+-----------------+--------------+--------------+ | 18:cab | p_2bc_2 | P_2_21_21 | P22121 | P22121 | +---------+-----------------+-----------------+--------------+--------------+ | 18:bca | p_2ac_2ac | P_21_2_21 | P21221 | P21221 | +---------+-----------------+-----------------+--------------+--------------+ | 19 | p_2ac_2ab | P_21_21_21 | P212121 | P212121 | +---------+-----------------+-----------------+--------------+--------------+ | 20 | c_2c_2 | C_2_2_21 | C2221 | C2221 | +---------+-----------------+-----------------+--------------+--------------+ | 20:cab | a_2a_2a | A_21_2_2 | A2122 | A2122 | +---------+-----------------+-----------------+--------------+--------------+ | 20:bca | b_2_2b | B_2_21_2 | B2212 | B2212 | +---------+-----------------+-----------------+--------------+--------------+ | 21 | c_2_2 | C_2_2_2 | C222 | C222 | +---------+-----------------+-----------------+--------------+--------------+ | 21:cab | a_2_2 | A_2_2_2 | A222 | A222 | +---------+-----------------+-----------------+--------------+--------------+ | 21:bca | b_2_2 | B_2_2_2 | B222 | B222 | +---------+-----------------+-----------------+--------------+--------------+ | 22 | f_2_2 | F_2_2_2 | F222 | F222 | +---------+-----------------+-----------------+--------------+--------------+ | 23 | i_2_2 | I_2_2_2 | I222 | I222 | +---------+-----------------+-----------------+--------------+--------------+ | 24 | i_2b_2c | I_21_21_21 | I212121 | I212121 | +---------+-----------------+-----------------+--------------+--------------+ | 25 | p_2\_-2 | P_m_m_2 | Pmm2 | Pmm2 | +---------+-----------------+-----------------+--------------+--------------+ | 25:cab | p\_-2_2 | P_2_m_m | P2mm | P2mm | +---------+-----------------+-----------------+--------------+--------------+ | 25:bca | p\_-2\_-2 | P_m_2_m | Pm2m | Pm2m | +---------+-----------------+-----------------+--------------+--------------+ | 26 | p_2c\_-2 | P_m_c_21 | Pmc21 | Pmc21 | +---------+-----------------+-----------------+--------------+--------------+ | 26:ba-c | p_2c\_-2c | P_c_m_21 | Pcm21 | Pcm21 | +---------+-----------------+-----------------+--------------+--------------+ | 26:cab | p\_-2a_2a | P_21_m_a | P21ma | P21ma | +---------+-----------------+-----------------+--------------+--------------+ | 26:-cba | p\_-2_2a | P_21_a_m | P21am | P21am | +---------+-----------------+-----------------+--------------+--------------+ | 26:bca | p\_-2\_-2b | P_b_21_m | Pb21m | Pb21m | +---------+-----------------+-----------------+--------------+--------------+ | 26:a-cb | p\_-2b\_-2 | P_m_21_b | Pm21b | Pm21b | +---------+-----------------+-----------------+--------------+--------------+ | 27 | p_2\_-2c | P_c_c_2 | Pcc2 | Pcc2 | +---------+-----------------+-----------------+--------------+--------------+ | 27:cab | p\_-2a_2 | P_2_a_a | P2aa | P2aa | +---------+-----------------+-----------------+--------------+--------------+ | 27:bca | p\_-2b\_-2b | P_b_2_b | Pb2b | Pb2b | +---------+-----------------+-----------------+--------------+--------------+ | 28 | p_2\_-2a | P_m_a_2 | Pma2 | Pma2 | +---------+-----------------+-----------------+--------------+--------------+ | 28:ba-c | p_2\_-2b | P_b_m_2 | Pbm2 | Pbm2 | +---------+-----------------+-----------------+--------------+--------------+ | 28:cab | p\_-2b_2 | P_2_m_b | P2mb | P2mb | +---------+-----------------+-----------------+--------------+--------------+ | 28:-cba | p\_-2c_2 | P_2_c_m | P2cm | P2cm | +---------+-----------------+-----------------+--------------+--------------+ | 28:bca | p\_-2c\_-2c | P_c_2_m | Pc2m | Pc2m | +---------+-----------------+-----------------+--------------+--------------+ | 28:a-cb | p\_-2a\_-2a | P_m_2_a | Pm2a | Pm2a | +---------+-----------------+-----------------+--------------+--------------+ | 29 | p_2c\_-2ac | P_c_a_21 | Pca21 | Pca21 | +---------+-----------------+-----------------+--------------+--------------+ | 29:ba-c | p_2c\_-2b | P_b_c_21 | Pbc21 | Pbc21 | +---------+-----------------+-----------------+--------------+--------------+ | 29:cab | p\_-2b_2a | P_21_a_b | P21ab | P21ab | +---------+-----------------+-----------------+--------------+--------------+ | 29:-cba | p\_-2ac_2a | P_21_c_a | P21ca | P21ca | +---------+-----------------+-----------------+--------------+--------------+ | 29:bca | p\_-2bc\_-2c | P_c_21_b | Pc21b | Pc21b | +---------+-----------------+-----------------+--------------+--------------+ | 29:a-cb | p\_-2a\_-2ab | P_b_21_a | Pb21a | Pb21a | +---------+-----------------+-----------------+--------------+--------------+ | 30 | p_2\_-2bc | P_n_c_2 | Pnc2 | Pnc2 | +---------+-----------------+-----------------+--------------+--------------+ | 30:ba-c | p_2\_-2ac | P_c_n_2 | Pcn2 | Pcn2 | +---------+-----------------+-----------------+--------------+--------------+ | 30:cab | p\_-2ac_2 | P_2_n_a | P2na | P2na | +---------+-----------------+-----------------+--------------+--------------+ | 30:-cba | p\_-2ab_2 | P_2_a_n | P2an | P2an | +---------+-----------------+-----------------+--------------+--------------+ | 30:bca | p\_-2ab\_-2ab | P_b_2_n | Pb2n | Pb2n | +---------+-----------------+-----------------+--------------+--------------+ | 30:a-cb | p\_-2bc\_-2bc | P_n_2_b | Pn2b | Pn2b | +---------+-----------------+-----------------+--------------+--------------+ | 31 | p_2ac\_-2 | P_m_n_21 | Pmn21 | Pmn21 | +---------+-----------------+-----------------+--------------+--------------+ | 31:ba-c | p_2bc\_-2bc | P_n_m_21 | Pnm21 | Pnm21 | +---------+-----------------+-----------------+--------------+--------------+ | 31:cab | p\_-2ab_2ab | P_21_m_n | P21mn | P21mn | +---------+-----------------+-----------------+--------------+--------------+ | 31:-cba | p\_-2_2ac | P_21_n_m | P21nm | P21nm | +---------+-----------------+-----------------+--------------+--------------+ | 31:bca | p\_-2\_-2bc | P_n_21_m | Pn21m | Pn21m | +---------+-----------------+-----------------+--------------+--------------+ | 31:a-cb | p\_-2ab\_-2 | P_m_21_n | Pm21n | Pm21n | +---------+-----------------+-----------------+--------------+--------------+ | 32 | p_2\_-2ab | P_b_a_2 | Pba2 | Pba2 | +---------+-----------------+-----------------+--------------+--------------+ | 32:cab | p\_-2bc_2 | P_2_c_b | P2cb | P2cb | +---------+-----------------+-----------------+--------------+--------------+ | 32:bca | p\_-2ac\_-2ac | P_c_2_a | Pc2a | Pc2a | +---------+-----------------+-----------------+--------------+--------------+ | 33 | p_2c\_-2n | P_n_a_21 | Pna21 | Pna21 | +---------+-----------------+-----------------+--------------+--------------+ | 33:ba-c | p_2c\_-2ab | P_b_n_21 | Pbn21 | Pbn21 | +---------+-----------------+-----------------+--------------+--------------+ | 33:cab | p\_-2bc_2a | P_21_n_b | P21nb | P21nb | +---------+-----------------+-----------------+--------------+--------------+ | 33:-cba | p\_-2n_2a | P_21_c_n | P21cn | P21cn | +---------+-----------------+-----------------+--------------+--------------+ | 33:bca | p\_-2n\_-2ac | P_c_21_n | Pc21n | Pc21n | +---------+-----------------+-----------------+--------------+--------------+ | 33:a-cb | p\_-2ac\_-2n | P_n_21_a | Pn21a | Pn21a | +---------+-----------------+-----------------+--------------+--------------+ | 34 | p_2\_-2n | P_n_n_2 | Pnn2 | Pnn2 | +---------+-----------------+-----------------+--------------+--------------+ | 34:cab | p\_-2n_2 | P_2_n_n | P2nn | P2nn | +---------+-----------------+-----------------+--------------+--------------+ | 34:bca | p\_-2n\_-2n | P_n_2_n | Pn2n | Pn2n | +---------+-----------------+-----------------+--------------+--------------+ | 35 | c_2\_-2 | C_m_m_2 | Cmm2 | Cmm2 | +---------+-----------------+-----------------+--------------+--------------+ | 35:cab | a\_-2_2 | A_2_m_m | A2mm | A2mm | +---------+-----------------+-----------------+--------------+--------------+ | 35:bca | b\_-2\_-2 | B_m_2_m | Bm2m | Bm2m | +---------+-----------------+-----------------+--------------+--------------+ | 36 | c_2c\_-2 | C_m_c_21 | Cmc21 | Cmc21 | +---------+-----------------+-----------------+--------------+--------------+ | 36:ba-c | c_2c\_-2c | C_c_m_21 | Ccm21 | Ccm21 | +---------+-----------------+-----------------+--------------+--------------+ | 36:cab | a\_-2a_2a | A_21_m_a | A21ma | A21ma | +---------+-----------------+-----------------+--------------+--------------+ | 36:-cba | a\_-2_2a | A_21_a_m | A21am | A21am | +---------+-----------------+-----------------+--------------+--------------+ | 36:bca | b\_-2\_-2b | B_b_21_m | Bb21m | Bb21m | +---------+-----------------+-----------------+--------------+--------------+ | 36:a-cb | b\_-2b\_-2 | B_m_21_b | Bm21b | Bm21b | +---------+-----------------+-----------------+--------------+--------------+ | 37 | c_2\_-2c | C_c_c_2 | Ccc2 | Ccc2 | +---------+-----------------+-----------------+--------------+--------------+ | 37:cab | a\_-2a_2 | A_2_a_a | A2aa | A2aa | +---------+-----------------+-----------------+--------------+--------------+ | 37:bca | b\_-2b\_-2b | B_b_2_b | Bb2b | Bb2b | +---------+-----------------+-----------------+--------------+--------------+ | 38 | a_2\_-2 | A_m_m_2 | Amm2 | Amm2 | +---------+-----------------+-----------------+--------------+--------------+ | 38:ba-c | b_2\_-2 | B_m_m_2 | Bmm2 | Bmm2 | +---------+-----------------+-----------------+--------------+--------------+ | 38:cab | b\_-2_2 | B_2_m_m | B2mm | B2mm | +---------+-----------------+-----------------+--------------+--------------+ | 38:-cba | c\_-2_2 | C_2_m_m | C2mm | C2mm | +---------+-----------------+-----------------+--------------+--------------+ | 38:bca | c\_-2\_-2 | C_m_2_m | Cm2m | Cm2m | +---------+-----------------+-----------------+--------------+--------------+ | 38:a-cb | a\_-2\_-2 | A_m_2_m | Am2m | Am2m | +---------+-----------------+-----------------+--------------+--------------+ | 39 | a_2\_-2b | A_e_m_2 | Aem2 | Aem2 | +---------+-----------------+-----------------+--------------+--------------+ | 39:ba-c | b_2\_-2a | B_m_a_2 | Bma2 | Bma2 | +---------+-----------------+-----------------+--------------+--------------+ | 39:cab | b\_-2a_2 | B_2_c_m | B2cm | B2cm | +---------+-----------------+-----------------+--------------+--------------+ | 39:-cba | c\_-2a_2 | C_2_m_b | C2mb | C2mb | +---------+-----------------+-----------------+--------------+--------------+ | 39:bca | c\_-2a\_-2a | C_m_2_a | Cm2a | Cm2a | +---------+-----------------+-----------------+--------------+--------------+ | 39:a-cb | a\_-2b\_-2b | A_c_2_m | Ac2m | Ac2m | +---------+-----------------+-----------------+--------------+--------------+ | 40 | a_2\_-2a | A_m_a_2 | Ama2 | Ama2 | +---------+-----------------+-----------------+--------------+--------------+ | 40:ba-c | b_2\_-2b | B_b_m_2 | Bbm2 | Bbm2 | +---------+-----------------+-----------------+--------------+--------------+ | 40:cab | b\_-2b_2 | B_2_m_b | B2mb | B2mb | +---------+-----------------+-----------------+--------------+--------------+ | 40:-cba | c\_-2c_2 | C_2_c_m | C2cm | C2cm | +---------+-----------------+-----------------+--------------+--------------+ | 40:bca | c\_-2c\_-2c | C_c_2_m | Cc2m | Cc2m | +---------+-----------------+-----------------+--------------+--------------+ | 40:a-cb | a\_-2a\_-2a | A_m_2_a | Am2a | Am2a | +---------+-----------------+-----------------+--------------+--------------+ | 41 | a_2\_-2ab | A_e_a_2 | Aea2 | Aea2 | +---------+-----------------+-----------------+--------------+--------------+ | 41:ba-c | b_2\_-2ab | B_b_a_2 | Bba2 | Bba2 | +---------+-----------------+-----------------+--------------+--------------+ | 41:cab | b\_-2ab_2 | B_2_c_b | B2cb | B2cb | +---------+-----------------+-----------------+--------------+--------------+ | 41:-cba | c\_-2ac_2 | C_2_c_b | C2cb | C2cb | +---------+-----------------+-----------------+--------------+--------------+ | 41:bca | c\_-2ac\_-2ac | C_c_2_a | Cc2a | Cc2a | +---------+-----------------+-----------------+--------------+--------------+ | 41:a-cb | a\_-2ab\_-2ab | A_c_2_a | Ac2a | Ac2a | +---------+-----------------+-----------------+--------------+--------------+ | 42 | f_2\_-2 | F_m_m_2 | Fmm2 | Fmm2 | +---------+-----------------+-----------------+--------------+--------------+ | 42:cab | f\_-2_2 | F_2_m_m | F2mm | F2mm | +---------+-----------------+-----------------+--------------+--------------+ | 42:bca | f\_-2\_-2 | F_m_2_m | Fm2m | Fm2m | +---------+-----------------+-----------------+--------------+--------------+ | 43 | f_2\_-2d | F_d_d_2 | Fdd2 | Fdd2 | +---------+-----------------+-----------------+--------------+--------------+ | 43:cab | f\_-2d_2 | F_2_d_d | F2dd | F2dd | +---------+-----------------+-----------------+--------------+--------------+ | 43:bca | f\_-2d\_-2d | F_d_2_d | Fd2d | Fd2d | +---------+-----------------+-----------------+--------------+--------------+ | 44 | i_2\_-2 | I_m_m_2 | Imm2 | Imm2 | +---------+-----------------+-----------------+--------------+--------------+ | 44:cab | i\_-2_2 | I_2_m_m | I2mm | I2mm | +---------+-----------------+-----------------+--------------+--------------+ | 44:bca | i\_-2\_-2 | I_m_2_m | Im2m | Im2m | +---------+-----------------+-----------------+--------------+--------------+ | 45 | i_2\_-2c | I_b_a_2 | Iba2 | Iba2 | +---------+-----------------+-----------------+--------------+--------------+ | 45:cab | i\_-2a_2 | I_2_c_b | I2cb | I2cb | +---------+-----------------+-----------------+--------------+--------------+ | 45:bca | i\_-2b\_-2b | I_c_2_a | Ic2a | Ic2a | +---------+-----------------+-----------------+--------------+--------------+ | 46 | i_2\_-2a | I_m_a_2 | Ima2 | Ima2 | +---------+-----------------+-----------------+--------------+--------------+ | 46:ba-c | i_2\_-2b | I_b_m_2 | Ibm2 | Ibm2 | +---------+-----------------+-----------------+--------------+--------------+ | 46:cab | i\_-2b_2 | I_2_m_b | I2mb | I2mb | +---------+-----------------+-----------------+--------------+--------------+ | 46:-cba | i\_-2c_2 | I_2_c_m | I2cm | I2cm | +---------+-----------------+-----------------+--------------+--------------+ | 46:bca | i\_-2c\_-2c | I_c_2_m | Ic2m | Ic2m | +---------+-----------------+-----------------+--------------+--------------+ | 46:a-cb | i\_-2a\_-2a | I_m_2_a | Im2a | Im2a | +---------+-----------------+-----------------+--------------+--------------+ | 47 | -p_2_2 | P_m_m_m | Pmmm | Pmmm | +---------+-----------------+-----------------+--------------+--------------+ | 48:1 | p_2_2\_-1n | P_n_n_n:1 | Pnnn:1 | Pnnn | +---------+-----------------+-----------------+--------------+--------------+ | 48:2 | -p_2ab_2bc | P_n_n_n:2 | Pnnn:2 | Pnnn | +---------+-----------------+-----------------+--------------+--------------+ | 49 | -p_2_2c | P_c_c_m | Pccm | Pccm | +---------+-----------------+-----------------+--------------+--------------+ | 49:cab | -p_2a_2 | P_m_a_a | Pmaa | Pmaa | +---------+-----------------+-----------------+--------------+--------------+ | 49:bca | -p_2b_2b | P_b_m_b | Pbmb | Pbmb | +---------+-----------------+-----------------+--------------+--------------+ | 50:1 | p_2_2\_-1ab | P_b_a_n:1 | Pban:1 | Pban | +---------+-----------------+-----------------+--------------+--------------+ | 50:2 | -p_2ab_2b | P_b_a_n:2 | Pban:2 | Pban | +---------+-----------------+-----------------+--------------+--------------+ | 50:1cab | p_2_2\_-1bc | P_n_c_b:1 | Pncb:1 | Pncb | +---------+-----------------+-----------------+--------------+--------------+ | 50:2cab | -p_2b_2bc | P_n_c_b:2 | Pncb:2 | Pncb | +---------+-----------------+-----------------+--------------+--------------+ | 50:1bca | p_2_2\_-1ac | P_c_n_a:1 | Pcna:1 | Pcna | +---------+-----------------+-----------------+--------------+--------------+ | 50:2bca | -p_2a_2c | P_c_n_a:2 | Pcna:2 | Pcna | +---------+-----------------+-----------------+--------------+--------------+ | 51 | -p_2a_2a | P_m_m_a | Pmma | Pmma | +---------+-----------------+-----------------+--------------+--------------+ | 51:ba-c | -p_2b_2 | P_m_m_b | Pmmb | Pmmb | +---------+-----------------+-----------------+--------------+--------------+ | 51:cab | -p_2_2b | P_b_m_m | Pbmm | Pbmm | +---------+-----------------+-----------------+--------------+--------------+ | 51:-cba | -p_2c_2c | P_c_m_m | Pcmm | Pcmm | +---------+-----------------+-----------------+--------------+--------------+ | 51:bca | -p_2c_2 | P_m_c_m | Pmcm | Pmcm | +---------+-----------------+-----------------+--------------+--------------+ | 51:a-cb | -p_2_2a | P_m_a_m | Pmam | Pmam | +---------+-----------------+-----------------+--------------+--------------+ | 52 | -p_2a_2bc | P_n_n_a | Pnna | Pnna | +---------+-----------------+-----------------+--------------+--------------+ | 52:ba-c | -p_2b_2n | P_n_n_b | Pnnb | Pnnb | +---------+-----------------+-----------------+--------------+--------------+ | 52:cab | -p_2n_2b | P_b_n_n | Pbnn | Pbnn | +---------+-----------------+-----------------+--------------+--------------+ | 52:-cba | -p_2ab_2c | P_c_n_n | Pcnn | Pcnn | +---------+-----------------+-----------------+--------------+--------------+ | 52:bca | -p_2ab_2n | P_n_c_n | Pncn | Pncn | +---------+-----------------+-----------------+--------------+--------------+ | 52:a-cb | -p_2n_2bc | P_n_a_n | Pnan | Pnan | +---------+-----------------+-----------------+--------------+--------------+ | 53 | -p_2ac_2 | P_m_n_a | Pmna | Pmna | +---------+-----------------+-----------------+--------------+--------------+ | 53:ba-c | -p_2bc_2bc | P_n_m_b | Pnmb | Pnmb | +---------+-----------------+-----------------+--------------+--------------+ | 53:cab | -p_2ab_2ab | P_b_m_n | Pbmn | Pbmn | +---------+-----------------+-----------------+--------------+--------------+ | 53:-cba | -p_2_2ac | P_c_n_m | Pcnm | Pcnm | +---------+-----------------+-----------------+--------------+--------------+ | 53:bca | -p_2_2bc | P_n_c_m | Pncm | Pncm | +---------+-----------------+-----------------+--------------+--------------+ | 53:a-cb | -p_2ab_2 | P_m_a_n | Pman | Pman | +---------+-----------------+-----------------+--------------+--------------+ | 54 | -p_2a_2ac | P_c_c_a | Pcca | Pcca | +---------+-----------------+-----------------+--------------+--------------+ | 54:ba-c | -p_2b_2c | P_c_c_b | Pccb | Pccb | +---------+-----------------+-----------------+--------------+--------------+ | 54:cab | -p_2a_2b | P_b_a_a | Pbaa | Pbaa | +---------+-----------------+-----------------+--------------+--------------+ | 54:-cba | -p_2ac_2c | P_c_a_a | Pcaa | Pcaa | +---------+-----------------+-----------------+--------------+--------------+ | 54:bca | -p_2bc_2b | P_b_c_b | Pbcb | Pbcb | +---------+-----------------+-----------------+--------------+--------------+ | 54:a-cb | -p_2b_2ab | P_b_a_b | Pbab | Pbab | +---------+-----------------+-----------------+--------------+--------------+ | 55 | -p_2_2ab | P_b_a_m | Pbam | Pbam | +---------+-----------------+-----------------+--------------+--------------+ | 55:cab | -p_2bc_2 | P_m_c_b | Pmcb | Pmcb | +---------+-----------------+-----------------+--------------+--------------+ | 55:bca | -p_2ac_2ac | P_c_m_a | Pcma | Pcma | +---------+-----------------+-----------------+--------------+--------------+ | 56 | -p_2ab_2ac | P_c_c_n | Pccn | Pccn | +---------+-----------------+-----------------+--------------+--------------+ | 56:cab | -p_2ac_2bc | P_n_a_a | Pnaa | Pnaa | +---------+-----------------+-----------------+--------------+--------------+ | 56:bca | -p_2bc_2ab | P_b_n_b | Pbnb | Pbnb | +---------+-----------------+-----------------+--------------+--------------+ | 57 | -p_2c_2b | P_b_c_m | Pbcm | Pbcm | +---------+-----------------+-----------------+--------------+--------------+ | 57:ba-c | -p_2c_2ac | P_c_a_m | Pcam | Pcam | +---------+-----------------+-----------------+--------------+--------------+ | 57:cab | -p_2ac_2a | P_m_c_a | Pmca | Pmca | +---------+-----------------+-----------------+--------------+--------------+ | 57:-cba | -p_2b_2a | P_m_a_b | Pmab | Pmab | +---------+-----------------+-----------------+--------------+--------------+ | 57:bca | -p_2a_2ab | P_b_m_a | Pbma | Pbma | +---------+-----------------+-----------------+--------------+--------------+ | 57:a-cb | -p_2bc_2c | P_c_m_b | Pcmb | Pcmb | +---------+-----------------+-----------------+--------------+--------------+ | 58 | -p_2_2n | P_n_n_m | Pnnm | Pnnm | +---------+-----------------+-----------------+--------------+--------------+ | 58:cab | -p_2n_2 | P_m_n_n | Pmnn | Pmnn | +---------+-----------------+-----------------+--------------+--------------+ | 58:bca | -p_2n_2n | P_n_m_n | Pnmn | Pnmn | +---------+-----------------+-----------------+--------------+--------------+ | 59:1 | p_2_2ab\_-1ab | P_m_m_n:1 | Pmmn:1 | Pmmn | +---------+-----------------+-----------------+--------------+--------------+ | 59:2 | -p_2ab_2a | P_m_m_n:2 | Pmmn:2 | Pmmn | +---------+-----------------+-----------------+--------------+--------------+ | 59:1cab | p_2bc_2\_-1bc | P_n_m_m:1 | Pnmm:1 | Pnmm | +---------+-----------------+-----------------+--------------+--------------+ | 59:2cab | -p_2c_2bc | P_n_m_m:2 | Pnmm:2 | Pnmm | +---------+-----------------+-----------------+--------------+--------------+ | 59:1bca | p_2ac_2ac\_-1ac | P_m_n_m:1 | Pmnm:1 | Pmnm | +---------+-----------------+-----------------+--------------+--------------+ | 59:2bca | -p_2c_2a | P_m_n_m:2 | Pmnm:2 | Pmnm | +---------+-----------------+-----------------+--------------+--------------+ | 60 | -p_2n_2ab | P_b_c_n | Pbcn | Pbcn | +---------+-----------------+-----------------+--------------+--------------+ | 60:ba-c | -p_2n_2c | P_c_a_n | Pcan | Pcan | +---------+-----------------+-----------------+--------------+--------------+ | 60:cab | -p_2a_2n | P_n_c_a | Pnca | Pnca | +---------+-----------------+-----------------+--------------+--------------+ | 60:-cba | -p_2bc_2n | P_n_a_b | Pnab | Pnab | +---------+-----------------+-----------------+--------------+--------------+ | 60:bca | -p_2ac_2b | P_b_n_a | Pbna | Pbna | +---------+-----------------+-----------------+--------------+--------------+ | 60:a-cb | -p_2b_2ac | P_c_n_b | Pcnb | Pcnb | +---------+-----------------+-----------------+--------------+--------------+ | 61 | -p_2ac_2ab | P_b_c_a | Pbca | Pbca | +---------+-----------------+-----------------+--------------+--------------+ | 61:ba-c | -p_2bc_2ac | P_c_a_b | Pcab | Pcab | +---------+-----------------+-----------------+--------------+--------------+ | 62 | -p_2ac_2n | P_n_m_a | Pnma | Pnma | +---------+-----------------+-----------------+--------------+--------------+ | 62:ba-c | -p_2bc_2a | P_m_n_b | Pmnb | Pmnb | +---------+-----------------+-----------------+--------------+--------------+ | 62:cab | -p_2c_2ab | P_b_n_m | Pbnm | Pbnm | +---------+-----------------+-----------------+--------------+--------------+ | 62:-cba | -p_2n_2ac | P_c_m_n | Pcmn | Pcmn | +---------+-----------------+-----------------+--------------+--------------+ | 62:bca | -p_2n_2a | P_m_c_n | Pmcn | Pmcn | +---------+-----------------+-----------------+--------------+--------------+ | 62:a-cb | -p_2c_2n | P_n_a_m | Pnam | Pnam | +---------+-----------------+-----------------+--------------+--------------+ | 63 | -c_2c_2 | C_m_c_m | Cmcm | Cmcm | +---------+-----------------+-----------------+--------------+--------------+ | 63:ba-c | -c_2c_2c | C_c_m_m | Ccmm | Ccmm | +---------+-----------------+-----------------+--------------+--------------+ | 63:cab | -a_2a_2a | A_m_m_a | Amma | Amma | +---------+-----------------+-----------------+--------------+--------------+ | 63:-cba | -a_2_2a | A_m_a_m | Amam | Amam | +---------+-----------------+-----------------+--------------+--------------+ | 63:bca | -b_2_2b | B_b_m_m | Bbmm | Bbmm | +---------+-----------------+-----------------+--------------+--------------+ | 63:a-cb | -b_2b_2 | B_m_m_b | Bmmb | Bmmb | +---------+-----------------+-----------------+--------------+--------------+ | 64 | -c_2ac_2 | C_m_c_e | Cmce | Cmce | +---------+-----------------+-----------------+--------------+--------------+ | 64:ba-c | -c_2ac_2ac | C_c_m_b | Ccmb | Ccmb | +---------+-----------------+-----------------+--------------+--------------+ | 64:cab | -a_2ab_2ab | A_b_m_a | Abma | Abma | +---------+-----------------+-----------------+--------------+--------------+ | 64:-cba | -a_2_2ab | A_c_a_m | Acam | Acam | +---------+-----------------+-----------------+--------------+--------------+ | 64:bca | -b_2_2ab | B_b_c_m | Bbcm | Bbcm | +---------+-----------------+-----------------+--------------+--------------+ | 64:a-cb | -b_2ab_2 | B_m_a_b | Bmab | Bmab | +---------+-----------------+-----------------+--------------+--------------+ | 65 | -c_2_2 | C_m_m_m | Cmmm | Cmmm | +---------+-----------------+-----------------+--------------+--------------+ | 65:cab | -a_2_2 | A_m_m_m | Ammm | Ammm | +---------+-----------------+-----------------+--------------+--------------+ | 65:bca | -b_2_2 | B_m_m_m | Bmmm | Bmmm | +---------+-----------------+-----------------+--------------+--------------+ | 66 | -c_2_2c | C_c_c_m | Cccm | Cccm | +---------+-----------------+-----------------+--------------+--------------+ | 66:cab | -a_2a_2 | A_m_a_a | Amaa | Amaa | +---------+-----------------+-----------------+--------------+--------------+ | 66:bca | -b_2b_2b | B_b_m_b | Bbmb | Bbmb | +---------+-----------------+-----------------+--------------+--------------+ | 67 | -c_2a_2 | C_m_m_e | Cmme | Cmme | +---------+-----------------+-----------------+--------------+--------------+ | 67:ba-c | -c_2a_2a | C_m_m_b | Cmmb | Cmmb | +---------+-----------------+-----------------+--------------+--------------+ | 67:cab | -a_2b_2b | A_b_m_m | Abmm | Abmm | +---------+-----------------+-----------------+--------------+--------------+ | 67:-cba | -a_2_2b | A_c_m_m | Acmm | Acmm | +---------+-----------------+-----------------+--------------+--------------+ | 67:bca | -b_2_2a | B_m_c_m | Bmcm | Bmcm | +---------+-----------------+-----------------+--------------+--------------+ | 67:a-cb | -b_2a_2 | B_m_a_m | Bmam | Bmam | +---------+-----------------+-----------------+--------------+--------------+ | 68:1 | c_2_2\_-1ac | C_c_c_e:1 | Ccce:1 | Ccce | +---------+-----------------+-----------------+--------------+--------------+ | 68:2 | -c_2a_2ac | C_c_c_e:2 | Ccce:2 | Ccce | +---------+-----------------+-----------------+--------------+--------------+ | 68:1ba- | c_2_2\_-1ac | C_c_c_b:1 | Cccb:1 | Cccb | +---------+-----------------+-----------------+--------------+--------------+ | 68:2ba- | -c_2a_2c | C_c_c_b:2 | Cccb:2 | Cccb | +---------+-----------------+-----------------+--------------+--------------+ | 68:1cab | a_2_2\_-1ab | A_b_a_a:1 | Abaa:1 | Abaa | +---------+-----------------+-----------------+--------------+--------------+ | 68:2cab | -a_2a_2b | A_b_a_a:2 | Abaa:2 | Abaa | +---------+-----------------+-----------------+--------------+--------------+ | 68:1-cb | a_2_2\_-1ab | A_c_a_a:1 | Acaa:1 | Acaa | +---------+-----------------+-----------------+--------------+--------------+ | 68:2-cb | -a_2ab_2b | A_c_a_a:2 | Acaa:2 | Acaa | +---------+-----------------+-----------------+--------------+--------------+ | 68:1bca | b_2_2\_-1ab | B_b_c_b:1 | Bbcb:1 | Bbcb | +---------+-----------------+-----------------+--------------+--------------+ | 68:2bca | -b_2ab_2b | B_b_c_b:2 | Bbcb:2 | Bbcb | +---------+-----------------+-----------------+--------------+--------------+ | 68:1a-c | b_2_2\_-1ab | B_b_a_b:1 | Bbab:1 | Bbab | +---------+-----------------+-----------------+--------------+--------------+ | 68:2a-c | -b_2b_2ab | B_b_a_b:2 | Bbab:2 | Bbab | +---------+-----------------+-----------------+--------------+--------------+ | 69 | -f_2_2 | F_m_m_m | Fmmm | Fmmm | +---------+-----------------+-----------------+--------------+--------------+ | 70:1 | f_2_2\_-1d | F_d_d_d:1 | Fddd:1 | Fddd | +---------+-----------------+-----------------+--------------+--------------+ | 70:2 | -f_2uv_2vw | F_d_d_d:2 | Fddd:2 | Fddd | +---------+-----------------+-----------------+--------------+--------------+ | 71 | -i_2_2 | I_m_m_m | Immm | Immm | +---------+-----------------+-----------------+--------------+--------------+ | 72 | -i_2_2c | I_b_a_m | Ibam | Ibam | +---------+-----------------+-----------------+--------------+--------------+ | 72:cab | -i_2a_2 | I_m_c_b | Imcb | Imcb | +---------+-----------------+-----------------+--------------+--------------+ | 72:bca | -i_2b_2b | I_c_m_a | Icma | Icma | +---------+-----------------+-----------------+--------------+--------------+ | 73 | -i_2b_2c | I_b_c_a | Ibca | Ibca | +---------+-----------------+-----------------+--------------+--------------+ | 73:ba-c | -i_2a_2b | I_c_a_b | Icab | Icab | +---------+-----------------+-----------------+--------------+--------------+ | 74 | -i_2b_2 | I_m_m_a | Imma | Imma | +---------+-----------------+-----------------+--------------+--------------+ | 74:ba-c | -i_2a_2a | I_m_m_b | Immb | Immb | +---------+-----------------+-----------------+--------------+--------------+ | 74:cab | -i_2c_2c | I_b_m_m | Ibmm | Ibmm | +---------+-----------------+-----------------+--------------+--------------+ | 74:-cba | -i_2_2b | I_c_m_m | Icmm | Icmm | +---------+-----------------+-----------------+--------------+--------------+ | 74:bca | -i_2_2a | I_m_c_m | Imcm | Imcm | +---------+-----------------+-----------------+--------------+--------------+ | 74:a-cb | -i_2c_2 | I_m_a_m | Imam | Imam | +---------+-----------------+-----------------+--------------+--------------+ | 75 | p_4 | P_4 | P4 | P4 | +---------+-----------------+-----------------+--------------+--------------+ | 76 | p_4w | P_41 | P41 | P41 | +---------+-----------------+-----------------+--------------+--------------+ | 77 | p_4c | P_42 | P42 | P42 | +---------+-----------------+-----------------+--------------+--------------+ | 78 | p_4cw | P_43 | P43 | P43 | +---------+-----------------+-----------------+--------------+--------------+ | 79 | i_4 | I_4 | I4 | I4 | +---------+-----------------+-----------------+--------------+--------------+ | 80 | i_4bw | I_41 | I41 | I41 | +---------+-----------------+-----------------+--------------+--------------+ | 81 | p\_-4 | P\_-4 | P-4 | P-4 | +---------+-----------------+-----------------+--------------+--------------+ | 82 | i\_-4 | I\_-4 | I-4 | I-4 | +---------+-----------------+-----------------+--------------+--------------+ | 83 | -p_4 | P_4/m | P4/m | P4/m | +---------+-----------------+-----------------+--------------+--------------+ | 84 | -p_4c | P_42/m | P42/m | P42/m | +---------+-----------------+-----------------+--------------+--------------+ | 85:1 | p_4ab\_-1ab | P_4/n:1 | P4/n:1 | P4/n | +---------+-----------------+-----------------+--------------+--------------+ | 85:2 | -p_4a | P_4/n:2 | P4/n:2 | P4/n | +---------+-----------------+-----------------+--------------+--------------+ | 86:1 | p_4n\_-1n | P_42/n:1 | P42/n:1 | P42/n | +---------+-----------------+-----------------+--------------+--------------+ | 86:2 | -p_4bc | P_42/n:2 | P42/n:2 | P42/n | +---------+-----------------+-----------------+--------------+--------------+ | 87 | -i_4 | I_4/m | I4/m | I4/m | +---------+-----------------+-----------------+--------------+--------------+ | 88:1 | i_4bw\_-1bw | I_41/a:1 | I41/a:1 | I41/a | +---------+-----------------+-----------------+--------------+--------------+ | 88:2 | -i_4ad | I_41/a:2 | I41/a:2 | I41/a | +---------+-----------------+-----------------+--------------+--------------+ | 89 | p_4_2 | P_4_2_2 | P422 | P422 | +---------+-----------------+-----------------+--------------+--------------+ | 90 | p_4ab_2ab | P_4_21_2 | P4212 | P4212 | +---------+-----------------+-----------------+--------------+--------------+ | 91 | p_4w_2c | P_41_2_2 | P4122 | P4122 | +---------+-----------------+-----------------+--------------+--------------+ | 92 | p_4abw_2nw | P_41_21_2 | P41212 | P41212 | +---------+-----------------+-----------------+--------------+--------------+ | 93 | p_4c_2 | P_42_2_2 | P4222 | P4222 | +---------+-----------------+-----------------+--------------+--------------+ | 94 | p_4n_2n | P_42_21_2 | P42212 | P42212 | +---------+-----------------+-----------------+--------------+--------------+ | 95 | p_4cw_2c | P_43_2_2 | P4322 | P4322 | +---------+-----------------+-----------------+--------------+--------------+ | 96 | p_4nw_2abw | P_43_21_2 | P43212 | P43212 | +---------+-----------------+-----------------+--------------+--------------+ | 97 | i_4_2 | I_4_2_2 | I422 | I422 | +---------+-----------------+-----------------+--------------+--------------+ | 98 | i_4bw_2bw | I_41_2_2 | I4122 | I4122 | +---------+-----------------+-----------------+--------------+--------------+ | 99 | p_4\_-2 | P_4_m_m | P4mm | P4mm | +---------+-----------------+-----------------+--------------+--------------+ | 100 | p_4\_-2ab | P_4_b_m | P4bm | P4bm | +---------+-----------------+-----------------+--------------+--------------+ | 101 | p_4c\_-2c | P_42_c_m | P42cm | P42cm | +---------+-----------------+-----------------+--------------+--------------+ | 102 | p_4n\_-2n | P_42_n_m | P42nm | P42nm | +---------+-----------------+-----------------+--------------+--------------+ | 103 | p_4\_-2c | P_4_c_c | P4cc | P4cc | +---------+-----------------+-----------------+--------------+--------------+ | 104 | p_4\_-2n | P_4_n_c | P4nc | P4nc | +---------+-----------------+-----------------+--------------+--------------+ | 105 | p_4c\_-2 | P_42_m_c | P42mc | P42mc | +---------+-----------------+-----------------+--------------+--------------+ | 106 | p_4c\_-2ab | P_42_b_c | P42bc | P42bc | +---------+-----------------+-----------------+--------------+--------------+ | 107 | i_4\_-2 | I_4_m_m | I4mm | I4mm | +---------+-----------------+-----------------+--------------+--------------+ | 108 | i_4\_-2c | I_4_c_m | I4cm | I4cm | +---------+-----------------+-----------------+--------------+--------------+ | 109 | i_4bw\_-2 | I_41_m_d | I41md | I41md | +---------+-----------------+-----------------+--------------+--------------+ | 110 | i_4bw\_-2c | I_41_c_d | I41cd | I41cd | +---------+-----------------+-----------------+--------------+--------------+ | 111 | p\_-4_2 | P\_-4_2_m | P-42m | P-42m | +---------+-----------------+-----------------+--------------+--------------+ | 112 | p\_-4_2c | P\_-4_2_c | P-42c | P-42c | +---------+-----------------+-----------------+--------------+--------------+ | 113 | p\_-4_2ab | P\_-4_21_m | P-421m | P-421m | +---------+-----------------+-----------------+--------------+--------------+ | 114 | p\_-4_2n | P\_-4_21_c | P-421c | P-421c | +---------+-----------------+-----------------+--------------+--------------+ | 115 | p\_-4\_-2 | P\_-4_m_2 | P-4m2 | P-4m2 | +---------+-----------------+-----------------+--------------+--------------+ | 116 | p\_-4\_-2c | P\_-4_c_2 | P-4c2 | P-4c2 | +---------+-----------------+-----------------+--------------+--------------+ | 117 | p\_-4\_-2ab | P\_-4_b_2 | P-4b2 | P-4b2 | +---------+-----------------+-----------------+--------------+--------------+ | 118 | p\_-4\_-2n | P\_-4_n_2 | P-4n2 | P-4n2 | +---------+-----------------+-----------------+--------------+--------------+ | 119 | i\_-4\_-2 | I\_-4_m_2 | I-4m2 | I-4m2 | +---------+-----------------+-----------------+--------------+--------------+ | 120 | i\_-4\_-2c | I\_-4_c_2 | I-4c2 | I-4c2 | +---------+-----------------+-----------------+--------------+--------------+ | 121 | i\_-4_2 | I\_-4_2_m | I-42m | I-42m | +---------+-----------------+-----------------+--------------+--------------+ | 122 | i\_-4_2bw | I\_-4_2_d | I-42d | I-42d | +---------+-----------------+-----------------+--------------+--------------+ | 123 | -p_4_2 | P_4/m_m_m | P4/mmm | P4/mmm | +---------+-----------------+-----------------+--------------+--------------+ | 124 | -p_4_2c | P_4/m_c_c | P4/mcc | P4/mcc | +---------+-----------------+-----------------+--------------+--------------+ | 125:1 | p_4_2\_-1ab | P_4/n_b_m:1 | P4/nbm:1 | P4/nbm | +---------+-----------------+-----------------+--------------+--------------+ | 125:2 | -p_4a_2b | P_4/n_b_m:2 | P4/nbm:2 | P4/nbm | +---------+-----------------+-----------------+--------------+--------------+ | 126:1 | p_4_2\_-1n | P_4/n_n_c:1 | P4/nnc:1 | P4/nnc | +---------+-----------------+-----------------+--------------+--------------+ | 126:2 | -p_4a_2bc | P_4/n_n_c:2 | P4/nnc:2 | P4/nnc | +---------+-----------------+-----------------+--------------+--------------+ | 127 | -p_4_2ab | P_4/m_b_m | P4/mbm | P4/mbm | +---------+-----------------+-----------------+--------------+--------------+ | 128 | -p_4_2n | P_4/m_n_c | P4/mnc | P4/mnc | +---------+-----------------+-----------------+--------------+--------------+ | 129:1 | p_4ab_2ab\_-1ab | P_4/n_m_m:1 | P4/nmm:1 | P4/nmm | +---------+-----------------+-----------------+--------------+--------------+ | 129:2 | -p_4a_2a | P_4/n_m_m:2 | P4/nmm:2 | P4/nmm | +---------+-----------------+-----------------+--------------+--------------+ | 130:1 | p_4ab_2n\_-1ab | P_4/n_c_c:1 | P4/ncc:1 | P4/ncc | +---------+-----------------+-----------------+--------------+--------------+ | 130:2 | -p_4a_2ac | P_4/n_c_c:2 | P4/ncc:2 | P4/ncc | +---------+-----------------+-----------------+--------------+--------------+ | 131 | -p_4c_2 | P_42/m_m_c | P42/mmc | P42/mmc | +---------+-----------------+-----------------+--------------+--------------+ | 132 | -p_4c_2c | P_42/m_c_m | P42/mcm | P42/mcm | +---------+-----------------+-----------------+--------------+--------------+ | 133:1 | p_4n_2c\_-1n | P_42/n_b_c:1 | P42/nbc:1 | P42/nbc | +---------+-----------------+-----------------+--------------+--------------+ | 133:2 | -p_4ac_2b | P_42/n_b_c:2 | P42/nbc:2 | P42/nbc | +---------+-----------------+-----------------+--------------+--------------+ | 134:1 | p_4n_2\_-1n | P_42/n_n_m:1 | P42/nnm:1 | P42/nnm | +---------+-----------------+-----------------+--------------+--------------+ | 134:2 | -p_4ac_2bc | P_42/n_n_m:2 | P42/nnm:2 | P42/nnm | +---------+-----------------+-----------------+--------------+--------------+ | 135 | -p_4c_2ab | P_42/m_b_c | P42/mbc | P42/mbc | +---------+-----------------+-----------------+--------------+--------------+ | 136 | -p_4n_2n | P_42/m_n_m | P42/mnm | P42/mnm | +---------+-----------------+-----------------+--------------+--------------+ | 137:1 | p_4n_2n\_-1n | P_42/n_m_c:1 | P42/nmc:1 | P42/nmc | +---------+-----------------+-----------------+--------------+--------------+ | 137:2 | -p_4ac_2a | P_42/n_m_c:2 | P42/nmc:2 | P42/nmc | +---------+-----------------+-----------------+--------------+--------------+ | 138:1 | p_4n_2ab\_-1n | P_42/n_c_m:1 | P42/ncm:1 | P42/ncm | +---------+-----------------+-----------------+--------------+--------------+ | 138:2 | -p_4ac_2ac | P_42/n_c_m:2 | P42/ncm:2 | P42/ncm | +---------+-----------------+-----------------+--------------+--------------+ | 139 | -i_4_2 | I_4/m_m_m | I4/mmm | I4/mmm | +---------+-----------------+-----------------+--------------+--------------+ | 140 | -i_4_2c | I_4/m_c_m | I4/mcm | I4/mcm | +---------+-----------------+-----------------+--------------+--------------+ | 141:1 | i_4bw_2bw\_-1bw | I_41/a_m_d:1 | I41/amd:1 | I41/amd | +---------+-----------------+-----------------+--------------+--------------+ | 141:2 | -i_4bd_2 | I_41/a_m_d:2 | I41/amd:2 | I41/amd | +---------+-----------------+-----------------+--------------+--------------+ | 142:1 | i_4bw_2aw\_-1bw | I_41/a_c_d:1 | I41/acd:1 | I41/acd | +---------+-----------------+-----------------+--------------+--------------+ | 142:2 | -i_4bd_2c | I_41/a_c_d:2 | I41/acd:2 | I41/acd | +---------+-----------------+-----------------+--------------+--------------+ | 143 | p_3 | P_3 | P3 | P3 | +---------+-----------------+-----------------+--------------+--------------+ | 144 | p_31 | P_31 | P31 | P31 | +---------+-----------------+-----------------+--------------+--------------+ | 145 | p_32 | P_32 | P32 | P32 | +---------+-----------------+-----------------+--------------+--------------+ | 146:h | r_3 | R_3:h | R3:h | R3 | +---------+-----------------+-----------------+--------------+--------------+ | 146:r | p_3* | R_3:r | R3:r | R3 | +---------+-----------------+-----------------+--------------+--------------+ | 147 | -p_3 | P\_-3 | P-3 | P-3 | +---------+-----------------+-----------------+--------------+--------------+ | 148:h | -r_3 | R\_-3:h | R-3:h | R-3 | +---------+-----------------+-----------------+--------------+--------------+ | 148:r | -p_3* | R\_-3:r | R-3:r | R-3 | +---------+-----------------+-----------------+--------------+--------------+ | 149 | p_3_2 | P_3_1_2 | P312 | P312 | +---------+-----------------+-----------------+--------------+--------------+ | 150 | p_3_2" | P_3_2_1 | P321 | P321 | +---------+-----------------+-----------------+--------------+--------------+ | 151 | p_31_2\_(0_0_4) | P_31_1_2 | P3112 | P3112 | +---------+-----------------+-----------------+--------------+--------------+ | 152 | p_31_2" | P_31_2_1 | P3121 | P3121 | +---------+-----------------+-----------------+--------------+--------------+ | 153 | p_32_2\_(0_0_2) | P_32_1_2 | P3212 | P3212 | +---------+-----------------+-----------------+--------------+--------------+ | 154 | p_32_2" | P_32_2_1 | P3221 | P3221 | +---------+-----------------+-----------------+--------------+--------------+ | 155:h | r_3_2" | R_3_2:h | R32:h | R32 | +---------+-----------------+-----------------+--------------+--------------+ | 155:r | p_3*_2 | R_3_2:r | R32:r | R32 | +---------+-----------------+-----------------+--------------+--------------+ | 156 | p_3\_-2" | P_3_m_1 | P3m1 | P3m1 | +---------+-----------------+-----------------+--------------+--------------+ | 157 | p_3\_-2 | P_3_1_m | P31m | P31m | +---------+-----------------+-----------------+--------------+--------------+ | 158 | p_3\_-2"c | P_3_c_1 | P3c1 | P3c1 | +---------+-----------------+-----------------+--------------+--------------+ | 159 | p_3\_-2c | P_3_1_c | P31c | P31c | +---------+-----------------+-----------------+--------------+--------------+ | 160:h | r_3\_-2" | R_3_m:h | R3m:h | R3m | +---------+-----------------+-----------------+--------------+--------------+ | 160:r | p_3*\_-2 | R_3_m:r | R3m:r | R3m | +---------+-----------------+-----------------+--------------+--------------+ | 161:h | r_3\_-2"c | R_3_c:h | R3c:h | R3c | +---------+-----------------+-----------------+--------------+--------------+ | 161:r | p_3*\_-2n | R_3_c:r | R3c:r | R3c | +---------+-----------------+-----------------+--------------+--------------+ | 162 | -p_3_2 | P\_-3_1_m | P-31m | P-31m | +---------+-----------------+-----------------+--------------+--------------+ | 163 | -p_3_2c | P\_-3_1_c | P-31c | P-31c | +---------+-----------------+-----------------+--------------+--------------+ | 164 | -p_3_2" | P\_-3_m_1 | P-3m1 | P-3m1 | +---------+-----------------+-----------------+--------------+--------------+ | 165 | -p_3_2"c | P\_-3_c_1 | P-3c1 | P-3c1 | +---------+-----------------+-----------------+--------------+--------------+ | 166:h | -r_3_2" | R\_-3_m:h | R-3m:h | R-3m | +---------+-----------------+-----------------+--------------+--------------+ | 166:r | -p_3*_2 | R\_-3_m:r | R-3m:r | R-3m | +---------+-----------------+-----------------+--------------+--------------+ | 167:h | -r_3_2"c | R\_-3_c:h | R-3c:h | R-3c | +---------+-----------------+-----------------+--------------+--------------+ | 167:r | -p_3*_2n | R\_-3_c:r | R-3c:r | R-3c | +---------+-----------------+-----------------+--------------+--------------+ | 168 | p_6 | P_6 | P6 | P6 | +---------+-----------------+-----------------+--------------+--------------+ | 169 | p_61 | P_61 | P61 | P61 | +---------+-----------------+-----------------+--------------+--------------+ | 170 | p_65 | P_65 | P65 | P65 | +---------+-----------------+-----------------+--------------+--------------+ | 171 | p_62 | P_62 | P62 | P62 | +---------+-----------------+-----------------+--------------+--------------+ | 172 | p_64 | P_64 | P64 | P64 | +---------+-----------------+-----------------+--------------+--------------+ | 173 | p_6c | P_63 | P63 | P63 | +---------+-----------------+-----------------+--------------+--------------+ | 174 | p\_-6 | P\_-6 | P-6 | P-6 | +---------+-----------------+-----------------+--------------+--------------+ | 175 | -p_6 | P_6/m | P6/m | P6/m | +---------+-----------------+-----------------+--------------+--------------+ | 176 | -p_6c | P_63/m | P63/m | P63/m | +---------+-----------------+-----------------+--------------+--------------+ | 177 | p_6_2 | P_6_2_2 | P622 | P622 | +---------+-----------------+-----------------+--------------+--------------+ | 178 | p_61_2\_(0_0_5) | P_61_2_2 | P6122 | P6122 | +---------+-----------------+-----------------+--------------+--------------+ | 179 | p_65_2\_(0_0_1) | P_65_2_2 | P6522 | P6522 | +---------+-----------------+-----------------+--------------+--------------+ | 180 | p_62_2\_(0_0_4) | P_62_2_2 | P6222 | P6222 | +---------+-----------------+-----------------+--------------+--------------+ | 181 | p_64_2\_(0_0_2) | P_64_2_2 | P6422 | P6422 | +---------+-----------------+-----------------+--------------+--------------+ | 182 | p_6c_2c | P_63_2_2 | P6322 | P6322 | +---------+-----------------+-----------------+--------------+--------------+ | 183 | p_6\_-2 | P_6_m_m | P6mm | P6mm | +---------+-----------------+-----------------+--------------+--------------+ | 184 | p_6\_-2c | P_6_c_c | P6cc | P6cc | +---------+-----------------+-----------------+--------------+--------------+ | 185 | p_6c\_-2 | P_63_c_m | P63cm | P63cm | +---------+-----------------+-----------------+--------------+--------------+ | 186 | p_6c\_-2c | P_63_m_c | P63mc | P63mc | +---------+-----------------+-----------------+--------------+--------------+ | 187 | p\_-6_2 | P\_-6_m_2 | P-6m2 | P-6m2 | +---------+-----------------+-----------------+--------------+--------------+ | 188 | p\_-6c_2 | P\_-6_c_2 | P-6c2 | P-6c2 | +---------+-----------------+-----------------+--------------+--------------+ | 189 | p\_-6\_-2 | P\_-6_2_m | P-62m | P-62m | +---------+-----------------+-----------------+--------------+--------------+ | 190 | p\_-6c\_-2c | P\_-6_2_c | P-62c | P-62c | +---------+-----------------+-----------------+--------------+--------------+ | 191 | -p_6_2 | P_6/m_m_m | P6/mmm | P6/mmm | +---------+-----------------+-----------------+--------------+--------------+ | 192 | -p_6_2c | P_6/m_c_c | P6/mcc | P6/mcc | +---------+-----------------+-----------------+--------------+--------------+ | 193 | -p_6c_2 | P_63/m_c_m | P63/mcm | P63/mcm | +---------+-----------------+-----------------+--------------+--------------+ | 194 | -p_6c_2c | P_63/m_m_c | P63/mmc | P63/mmc | +---------+-----------------+-----------------+--------------+--------------+ | 195 | p_2_2_3 | P_2_3 | P23 | P23 | +---------+-----------------+-----------------+--------------+--------------+ | 196 | f_2_2_3 | F_2_3 | F23 | F23 | +---------+-----------------+-----------------+--------------+--------------+ | 197 | i_2_2_3 | I_2_3 | I23 | I23 | +---------+-----------------+-----------------+--------------+--------------+ | 198 | p_2ac_2ab_3 | P_21_3 | P213 | P213 | +---------+-----------------+-----------------+--------------+--------------+ | 199 | i_2b_2c_3 | I_21_3 | I213 | I213 | +---------+-----------------+-----------------+--------------+--------------+ | 200 | -p_2_2_3 | P_m\_-3 | Pm-3 | Pm-3 | +---------+-----------------+-----------------+--------------+--------------+ | 201:1 | p_2_2_3\_-1n | P_n\_-3:1 | Pn-3:1 | Pn-3 | +---------+-----------------+-----------------+--------------+--------------+ | 201:2 | -p_2ab_2bc_3 | P_n\_-3:2 | Pn-3:2 | Pn-3 | +---------+-----------------+-----------------+--------------+--------------+ | 202 | -f_2_2_3 | F_m\_-3 | Fm-3 | Fm-3 | +---------+-----------------+-----------------+--------------+--------------+ | 203:1 | f_2_2_3\_-1d | F_d\_-3:1 | Fd-3:1 | Fd-3 | +---------+-----------------+-----------------+--------------+--------------+ | 203:2 | -f_2uv_2vw_3 | F_d\_-3:2 | Fd-3:2 | Fd-3 | +---------+-----------------+-----------------+--------------+--------------+ | 204 | -i_2_2_3 | I_m\_-3 | Im-3 | Im-3 | +---------+-----------------+-----------------+--------------+--------------+ | 205 | -p_2ac_2ab_3 | P_a\_-3 | Pa-3 | Pa-3 | +---------+-----------------+-----------------+--------------+--------------+ | 206 | -i_2b_2c_3 | I_a\_-3 | Ia-3 | Ia-3 | +---------+-----------------+-----------------+--------------+--------------+ | 207 | p_4_2_3 | P_4_3_2 | P432 | P432 | +---------+-----------------+-----------------+--------------+--------------+ | 208 | p_4n_2_3 | P_42_3_2 | P4232 | P4232 | +---------+-----------------+-----------------+--------------+--------------+ | 209 | f_4_2_3 | F_4_3_2 | F432 | F432 | +---------+-----------------+-----------------+--------------+--------------+ | 210 | f_4d_2_3 | F_41_3_2 | F4132 | F4132 | +---------+-----------------+-----------------+--------------+--------------+ | 211 | i_4_2_3 | I_4_3_2 | I432 | I432 | +---------+-----------------+-----------------+--------------+--------------+ | 212 | p_4acd_2ab_3 | P_43_3_2 | P4332 | P4332 | +---------+-----------------+-----------------+--------------+--------------+ | 213 | p_4bd_2ab_3 | P_41_3_2 | P4132 | P4132 | +---------+-----------------+-----------------+--------------+--------------+ | 214 | i_4bd_2c_3 | I_41_3_2 | I4132 | I4132 | +---------+-----------------+-----------------+--------------+--------------+ | 215 | p\_-4_2_3 | P\_-4_3_m | P-43m | P-43m | +---------+-----------------+-----------------+--------------+--------------+ | 216 | f\_-4_2_3 | F\_-4_3_m | F-43m | F-43m | +---------+-----------------+-----------------+--------------+--------------+ | 217 | i\_-4_2_3 | I\_-4_3_m | I-43m | I-43m | +---------+-----------------+-----------------+--------------+--------------+ | 218 | p\_-4n_2_3 | P\_-4_3_n | P-43n | P-43n | +---------+-----------------+-----------------+--------------+--------------+ | 219 | f\_-4a_2_3 | F\_-4_3_c | F-43c | F-43c | +---------+-----------------+-----------------+--------------+--------------+ | 220 | i\_-4bd_2c_3 | I\_-4_3_d | I-43d | I-43d | +---------+-----------------+-----------------+--------------+--------------+ | 221 | -p_4_2_3 | P_m\_-3_m | Pm-3m | Pm-3m | +---------+-----------------+-----------------+--------------+--------------+ | 222:1 | p_4_2_3\_-1n | P_n\_-3_n:1 | Pn-3n:1 | Pn-3n | +---------+-----------------+-----------------+--------------+--------------+ | 222:2 | -p_4a_2bc_3 | P_n\_-3_n:2 | Pn-3n:2 | Pn-3n | +---------+-----------------+-----------------+--------------+--------------+ | 223 | -p_4n_2_3 | P_m\_-3_n | Pm-3n | Pm-3n | +---------+-----------------+-----------------+--------------+--------------+ | 224:1 | p_4n_2_3\_-1n | P_n\_-3_m:1 | Pn-3m:1 | Pn-3m | +---------+-----------------+-----------------+--------------+--------------+ | 224:2 | -p_4bc_2bc_3 | P_n\_-3_m:2 | Pn-3m:2 | Pn-3m | +---------+-----------------+-----------------+--------------+--------------+ | 225 | -f_4_2_3 | F_m\_-3_m | Fm-3m | Fm-3m | +---------+-----------------+-----------------+--------------+--------------+ | 226 | -f_4a_2_3 | F_m\_-3_c | Fm-3c | Fm-3c | +---------+-----------------+-----------------+--------------+--------------+ | 227:1 | f_4d_2_3\_-1d | F_d\_-3_m:1 | Fd-3m:1 | Fd-3m | +---------+-----------------+-----------------+--------------+--------------+ | 227:2 | -f_4vw_2vw_3 | F_d\_-3_m:2 | Fd-3m:2 | Fd-3m | +---------+-----------------+-----------------+--------------+--------------+ | 228:1 | f_4d_2_3\_-1ad | F_d\_-3_c:1 | Fd-3c:1 | Fd-3c | +---------+-----------------+-----------------+--------------+--------------+ | 228:2 | -f_4ud_2vw_3 | F_d\_-3_c:2 | Fd-3c:2 | Fd-3c | +---------+-----------------+-----------------+--------------+--------------+ | 229 | -i_4_2_3 | I_m\_-3_m | Im-3m | Im-3m | +---------+-----------------+-----------------+--------------+--------------+ | 230 | -i_4bd_2c_3 | I_a\_-3_d | Ia-3d | Ia-3d | +---------+-----------------+-----------------+--------------+--------------+