Polytope of Type {9,4}
Play with this polytope as a twisty puzzle
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,4}*1152
if this polytope has a name.
Group : SmallGroup(1152,157853)
Rank : 3
Schlafli Type : {9,4}
Number of vertices, edges, etc : 144, 288, 64
Order of s0s1s2 : 9
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
P/N, where N=<s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 2.
32 facets:
32 of {9}*18
72 vertex figures:
72 of {4}*8
P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0> of order 2.
32 facets:
32 of {9}*18
80 vertex figures:
64 of {4}*8
16 of {2}*4
P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1> of order 2.
32 facets:
32 of {9}*18
72 vertex figures:
72 of {4}*8
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 2.
32 facets:
32 of {9}*18
72 vertex figures:
72 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
32 facets:
32 of {9}*18
72 vertex figures:
72 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1> of order 2.
32 facets:
32 of {9}*18
72 vertex figures:
72 of {4}*8
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1> of order 4.
16 facets:
16 of {9}*18
40 vertex figures:
32 of {4}*8
8 of {2}*4
P/N, where N=<s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1> of order 4.
16 facets:
16 of {9}*18
44 vertex figures:
28 of {4}*8
16 of {2}*4
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
16 facets:
16 of {9}*18
40 vertex figures:
32 of {4}*8
8 of {2}*4
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1> of order 4.
16 facets:
16 of {9}*18
40 vertex figures:
32 of {4}*8
8 of {2}*4
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1> of order 4.
16 facets:
16 of {9}*18
40 vertex figures:
8 of {2}*4
32 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0> of order 4.
16 facets:
16 of {9}*18
40 vertex figures:
32 of {4}*8
8 of {2}*4
P/N, where N=<s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0> of order 4.
16 facets:
16 of {9}*18
44 vertex figures:
28 of {4}*8
16 of {2}*4
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
16 facets:
16 of {9}*18
40 vertex figures:
32 of {4}*8
8 of {2}*4
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1, s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0> of order 4.
16 facets:
16 of {9}*18
40 vertex figures:
32 of {4}*8
8 of {2}*4
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1> of order 4.
16 facets:
16 of {9}*18
48 vertex figures:
24 of {4}*8
24 of {2}*4
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1> of order 4.
16 facets:
16 of {9}*18
40 vertex figures:
32 of {4}*8
8 of {2}*4
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1> of order 4.
16 facets:
16 of {9}*18
40 vertex figures:
32 of {4}*8
8 of {2}*4
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1> of order 4.
16 facets:
16 of {9}*18
40 vertex figures:
32 of {4}*8
8 of {2}*4
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1, s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0> of order 4.
16 facets:
16 of {9}*18
44 vertex figures:
16 of {2}*4
28 of {4}*8
P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2> of order 4.
16 facets:
16 of {9}*18
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 8.
8 facets:
8 of {9}*18
24 vertex figures:
12 of {4}*8
12 of {2}*4
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 8.
8 facets:
8 of {9}*18
20 vertex figures:
16 of {4}*8
4 of {2}*4
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0> of order 8.
8 facets:
8 of {9}*18
24 vertex figures:
12 of {4}*8
12 of {2}*4
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 8.
8 facets:
8 of {9}*18
20 vertex figures:
16 of {4}*8
4 of {2}*4
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s2, s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 8.
8 facets:
8 of {9}*18
18 vertex figures:
18 of {4}*8
P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 8.
8 facets:
8 of {9}*18
22 vertex figures:
14 of {4}*8
8 of {2}*4
P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 8.
8 facets:
8 of {9}*18
20 vertex figures:
16 of {4}*8
4 of {2}*4
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2> of order 8.
8 facets:
8 of {9}*18
20 vertex figures:
16 of {4}*8
4 of {2}*4
P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 8.
8 facets:
8 of {9}*18
22 vertex figures:
14 of {4}*8
8 of {2}*4
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 8.
8 facets:
8 of {9}*18
22 vertex figures:
14 of {4}*8
8 of {2}*4
P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1> of order 8.
8 facets:
8 of {9}*18
26 vertex figures:
16 of {2}*4
10 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 8.
8 facets:
8 of {9}*18
18 vertex figures:
18 of {4}*8
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 8.
8 facets:
8 of {9}*18
18 vertex figures:
18 of {4}*8
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1> of order 8.
8 facets:
8 of {9}*18
20 vertex figures:
16 of {4}*8
4 of {2}*4
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2> of order 8.
8 facets:
8 of {9}*18
20 vertex figures:
16 of {4}*8
4 of {2}*4
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0> of order 8.
8 facets:
8 of {9}*18
18 vertex figures:
18 of {4}*8
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2> of order 8.
8 facets:
8 of {9}*18
18 vertex figures:
18 of {4}*8
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 8.
8 facets:
8 of {9}*18
18 vertex figures:
18 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 8.
8 facets:
8 of {9}*18
20 vertex figures:
16 of {4}*8
4 of {2}*4
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 8.
8 facets:
8 of {9}*18
22 vertex figures:
14 of {4}*8
8 of {2}*4
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1> of order 8.
8 facets:
8 of {9}*18
20 vertex figures:
16 of {4}*8
4 of {2}*4
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1> of order 8.
8 facets:
8 of {9}*18
20 vertex figures:
16 of {4}*8
4 of {2}*4
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0> of order 8.
8 facets:
8 of {9}*18
22 vertex figures:
14 of {4}*8
8 of {2}*4
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1> of order 8.
8 facets:
8 of {9}*18
20 vertex figures:
16 of {4}*8
4 of {2}*4
P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 8.
8 facets:
8 of {9}*18
18 vertex figures:
18 of {4}*8
P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 8.
8 facets:
8 of {9}*18
18 vertex figures:
18 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1> of order 8.
8 facets:
8 of {9}*18
20 vertex figures:
16 of {4}*8
4 of {2}*4
P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1> of order 8.
8 facets:
8 of {9}*18
22 vertex figures:
8 of {2}*4
14 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1> of order 8.
8 facets:
8 of {9}*18
22 vertex figures:
14 of {4}*8
8 of {2}*4
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1> of order 8.
8 facets:
8 of {9}*18
20 vertex figures:
16 of {4}*8
4 of {2}*4
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1> of order 8.
8 facets:
8 of {9}*18
24 vertex figures:
12 of {4}*8
12 of {2}*4
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 8.
8 facets:
8 of {9}*18
22 vertex figures:
14 of {4}*8
8 of {2}*4
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0> of order 8.
8 facets:
8 of {9}*18
18 vertex figures:
18 of {4}*8
P/N, where N=<s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2, s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 8.
8 facets:
8 of {9}*18
18 vertex figures:
18 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 8.
8 facets:
8 of {9}*18
20 vertex figures:
16 of {4}*8
4 of {2}*4
P/N, where N=<s1*s2*s1*s2, s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0> of order 16.
4 facets:
4 of {9}*18
15 vertex figures:
12 of {2}*4
3 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0, s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1> of order 16.
4 facets:
4 of {9}*18
14 vertex figures:
4 of {4}*8
10 of {2}*4
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1> of order 16.
4 facets:
4 of {9}*18
11 vertex figures:
7 of {4}*8
4 of {2}*4
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s2, s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1> of order 16.
4 facets:
4 of {9}*18
9 vertex figures:
9 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0, s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2> of order 16.
4 facets:
4 of {9}*18
12 vertex figures:
6 of {4}*8
6 of {2}*4
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1> of order 16.
4 facets:
4 of {9}*18
11 vertex figures:
7 of {4}*8
4 of {2}*4
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5,17)( 6,18)( 7,20)( 8,19)( 9,49)(10,50)(11,52)(12,51)(13,33)(14,34)(15,36)(16,35)(23,24)(25,53)(26,54)(27,56)(28,55)(29,37)(30,38)(31,40)(32,39)(41,61)(42,62)(43,64)(44,63)(47,48)(59,60);;
s1 := ( 2,33)( 3,49)( 4,17)( 6,37)( 7,53)( 8,21)( 9,13)(10,45)(11,61)(12,29)(14,41)(15,57)(16,25)(18,36)(19,52)(22,40)(23,56)(26,48)(27,64)(28,32)(30,44)(31,60)(35,50)(39,54)(42,46)(43,62)(47,58)(59,63);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(64)!( 3, 4)( 5,17)( 6,18)( 7,20)( 8,19)( 9,49)(10,50)(11,52)(12,51)(13,33)(14,34)(15,36)(16,35)(23,24)(25,53)(26,54)(27,56)(28,55)(29,37)(30,38)(31,40)(32,39)(41,61)(42,62)(43,64)(44,63)(47,48)(59,60);
s1 := Sym(64)!( 2,33)( 3,49)( 4,17)( 6,37)( 7,53)( 8,21)( 9,13)(10,45)(11,61)(12,29)(14,41)(15,57)(16,25)(18,36)(19,52)(22,40)(23,56)(26,48)(27,64)(28,32)(30,44)(31,60)(35,50)(39,54)(42,46)(43,62)(47,58)(59,63);
s2 := Sym(64)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64);
poly := sub<Sym(64)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2 >;
References : None.
to this polytope
Twisty Puzzle