def get_faces(self):
"""Compute the indices of the faces (and other information we will need).
"""
for i, j in combinations(self.gens, 2):
# this is the center of the initial face,
# it's a vertex of the fundamental triangle.
c0 = self.triangle_verts[self.vertex_at_mirrors(i, j)]
# a list holds the vertices of the initial face.
f0 = []
m = self.cox_mat[i][j]
# this is the stabilizing subgroup of the initial face f0.
H = (i, j) + self.get_orthogonal_stabilizing_mirrors((i, j))
# type indicates if this face is regular (0) or truncated (1).
# it's truncated if and only if both mirrors are active.
type = 0
# compute the words (may not be in normal form) for the
# vertices of the initial face
if self.active[i] and self.active[j]:
type = 1
for k in range(m):
f0.append(self.G.move(self.vtable, 0, (i, j) * k))
f0.append(self.G.move(self.vtable, 0, (i, j) * k + (i, )))
elif self.active[i] and m > 2:
for k in range(m):
f0.append(self.G.move(self.vtable, 0, (j, i) * k))
elif self.active[j] and m > 2:
for k in range(m):
f0.append(self.G.move(self.vtable, 0, (i, j) * k))
else:
continue
# compute coset representatives of the initial face,
# each word in the result set maps f0 to a different face.
reps = set(self.word_generator(parabolic=H))
# sort the faces in shortlex order.
reps = self.G.sort_words(reps)
# a set holds faces, we use a set here because though a word w
# in H stabilizes f0, it may change cyclically rotate f0 to another
# different ordered tuple.
flist = []
for word in reps:
# compute the indices of the vertices of the transformed face
f = tuple(self.G.move(self.vtable, v, word) for v in f0)
# check if `None` is in f (in this case f contains some
# vertex that is not in the vertices list) or there already has
# a rotated version of f in the set.
if None not in f:
center = self.transform(word, c0)
coords = [self.vertices_coords[k] for k in f]
face = DihedralFace(word, f, center, coords, type)
flist.append(face)
self.face_indices[(i, j)] = flist
self.num_faces = sum(len(L) for L in self.face_indices.values())
def get_faces(self):
for i, j in combinations(self.gens, 2):
c0 = self.triangle_verts[self.vertex_at_mirrors(i, j)]
f0 = []
m = self.cox_mat[i][j]
H = (i, j)
type = 0
if self.active[i] and self.active[j]:
type = 1
for k in range(m):
f0.append(self.G.move(self.vtable, 0, (i, j) * k))
f0.append(self.G.move(self.vtable, 0, (i, j) * k + (i, )))
elif self.active[i] and m > 2:
for k in range(m):
f0.append(self.G.move(self.vtable, 0, (j, i) * k))
elif self.active[j] and m > 2:
for k in range(m):
f0.append(self.G.move(self.vtable, 0, (i, j) * k))
else:
continue
reps = set(
self.G.get_coset_representative(w, H) for w in self.words)
reps = self.G.sort_words(reps)
flist = []
for word in reps:
f = tuple(self.G.move(self.vtable, v, word) for v in f0)
if None not in f and not helpers.check_duplicate_face(
f, flist):
center = self.transform(word, c0)
coords = [self.vertices_coords[k] for k in f]
face = DihedralFace(word, f, center, coords, type)
flist.append(face)
self.face_indices[(i, j)] = flist
self.num_faces = sum(len(L) for L in self.face_indices.values())