<filename>bin/Python27/Lib/site-packages/sympy/combinatorics/tests/test_polyhedron.py
from sympy import symbols, FiniteSet
from sympy.combinatorics.polyhedron import (Polyhedron,
    tetrahedron, cube as square, octahedron, dodecahedron, icosahedron,
    cube_faces)
from sympy.combinatorics.permutations import Permutation
from sympy.combinatorics.perm_groups import PermutationGroup
from sympy.utilities.pytest import raises

rmul = Permutation.rmul

def test_polyhedron():
    raises(ValueError, lambda: Polyhedron(list('ab'),
        pgroup=[Permutation([0])]))
    pgroup = [Permutation([[0,7,2,5],[6,1,4,3]]),\
              Permutation([[0,7,1,6],[5,2,4,3]]),\
              Permutation([[3,6,0,5],[4,1,7,2]]),\
              Permutation([[7,4,5],[1,3,0],[2],[6]]),\
              Permutation([[1,3,2],[7,6,5],[4],[0]]),\
              Permutation([[4,7,6],[2,0,3],[1],[5]]),\
              Permutation([[1,2,0],[4,5,6],[3],[7]]),\
              Permutation([[4,2],[0,6],[3,7],[1,5]]),\
              Permutation([[3,5],[7,1],[2,6],[0,4]]),\
              Permutation([[2,5],[1,6],[0,4],[3,7]]),\
              Permutation([[4,3],[7,0],[5,1],[6,2]]),\
              Permutation([[4,1],[0,5],[6,2],[7,3]]),\
              Permutation([[7,2],[3,6],[0,4],[1,5]]),\
              Permutation([0,1,2,3,4,5,6,7])]
    corners = tuple(symbols('A:H'))
    faces = cube_faces
    cube = Polyhedron(corners, faces, pgroup)

    assert cube.edges == FiniteSet(*(
        (0, 1), (6, 7), (1, 2), (5, 6), (0, 3), (2, 3),
        (4, 7), (4, 5), (3, 7), (1, 5), (0, 4), (2, 6)))

    for i in xrange(3):    #  add 180 degree face rotations
        cube.rotate(cube.pgroup[i]**2)

    assert cube.corners == corners

    for i in range(3,7):  # add 240 degree axial corner rotations
        cube.rotate(cube.pgroup[i]**2)

    assert cube.corners == corners
    cube.rotate(1)
    raises(ValueError, lambda: cube.rotate(Permutation([0, 1])))
    assert cube.corners != corners
    assert cube.array_form == [7, 6, 4, 5, 3, 2, 0, 1]
    assert cube.cyclic_form == [[0, 7, 1, 6], [2, 4, 3, 5]]
    cube.reset()
    assert cube.corners == corners

    def check(h, size, rpt, target):

        assert len(h.faces) + len(h.vertices) - len(h.edges) == 2
        assert h.size == size

        got = set()
        for p in h.pgroup:
            # make sure it restores original
            P = h.copy()
            hit = P.corners
            for i in range(rpt):
                P.rotate(p)
                if P.corners == hit:
                    break
            else:
                print 'error in permutation', p.array_form
            for i in range(rpt):
                P.rotate(p)
                got.add(tuple(P.corners))
                c = P.corners
                f = [[c[i] for i in f] for f in P.faces]
                assert h.faces == Polyhedron(c, f).faces
        assert len(got) == target
        assert PermutationGroup([Permutation(g) for g in got]).is_group()

    for h, size, rpt, target in zip(
        (tetrahedron, square, octahedron, dodecahedron, icosahedron),
        (4,           8,      6,          20,          12),
        (3,           4,      4,          5,            5),
        (12,          24,     24,         60,           60)):
        check(h, size, rpt, target)
