Polytope of Type {4,4}
Play with this polytope as a twisty puzzle
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4}*1152
Also Known As : {4,4}(12,0), {4,4|12}. if this polytope has another name.
Group : SmallGroup(1152,32554)
Rank : 3
Schlafli Type : {4,4}
Number of vertices, edges, etc : 144, 288, 144
Order of s0s1s2 : 24
Order of s0s1s2s1 : 12
Special Properties :
Toroidal
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Halving Operation
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,4}*576
4-fold quotients : {4,4}*288
8-fold quotients : {4,4}*144
9-fold quotients : {4,4}*128
16-fold quotients : {4,4}*72
18-fold quotients : {4,4}*64
36-fold quotients : {4,4}*32
72-fold quotients : {2,4}*16, {4,2}*16
144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 2.
72 facets:
72 of {4}*8
72 vertex figures:
72 of {4}*8
P/N, where N=<s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 2.
72 facets:
72 of {4}*8
72 vertex figures:
72 of {4}*8
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0> of order 2.
72 facets:
72 of {4}*8
74 vertex figures:
70 of {4}*8
4 of {2}*4
P/N, where N=<s0*s1*s0*s1> of order 2.
74 facets:
4 of {2}*4
70 of {4}*8
72 vertex figures:
72 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
72 facets:
72 of {4}*8
72 vertex figures:
72 of {4}*8
P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 3.
48 facets:
48 of {4}*8
48 vertex figures:
48 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 3.
48 facets:
48 of {4}*8
48 vertex figures:
48 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0> of order 4.
36 facets:
36 of {4}*8
38 vertex figures:
34 of {4}*8
4 of {2}*4
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 4.
36 facets:
36 of {4}*8
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2> of order 4.
36 facets:
36 of {4}*8
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
36 facets:
36 of {4}*8
36 vertex figures:
36 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 4.
36 facets:
36 of {4}*8
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
36 facets:
36 of {4}*8
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 4.
36 facets:
36 of {4}*8
37 vertex figures:
35 of {4}*8
2 of {2}*4
P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
38 facets:
4 of {2}*4
34 of {4}*8
36 vertex figures:
36 of {4}*8
P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 4.
37 facets:
2 of {2}*4
35 of {4}*8
36 vertex figures:
36 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
36 facets:
36 of {4}*8
36 vertex figures:
36 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1> of order 6.
24 facets:
24 of {4}*8
24 vertex figures:
24 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2, s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 6.
24 facets:
24 of {4}*8
26 vertex figures:
22 of {4}*8
4 of {2}*4
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 6.
24 facets:
24 of {4}*8
24 vertex figures:
24 of {4}*8
P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 6.
26 facets:
4 of {2}*4
22 of {4}*8
24 vertex figures:
24 of {4}*8
P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0> of order 6.
24 facets:
24 of {4}*8
26 vertex figures:
4 of {2}*4
22 of {4}*8
P/N, where N=<s0*s1*s0*s1, s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 6.
26 facets:
4 of {2}*4
22 of {4}*8
24 vertex figures:
24 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 6.
24 facets:
24 of {4}*8
24 vertex figures:
24 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 6.
24 facets:
24 of {4}*8
24 vertex figures:
24 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 6.
24 facets:
24 of {4}*8
24 vertex figures:
24 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 6.
24 facets:
24 of {4}*8
24 vertex figures:
24 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 6.
24 facets:
24 of {4}*8
24 vertex figures:
24 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 8.
18 facets:
18 of {4}*8
18 vertex figures:
18 of {4}*8
P/N, where N=<s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2, s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 8.
18 facets:
18 of {4}*8
19 vertex figures:
17 of {4}*8
2 of {2}*4
P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 8.
19 facets:
2 of {2}*4
17 of {4}*8
18 vertex figures:
18 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s2*s1> of order 12.
12 facets:
12 of {4}*8
12 vertex figures:
12 of {4}*8
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 12.
12 facets:
12 of {4}*8
12 vertex figures:
12 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 12.
12 facets:
12 of {4}*8
12 vertex figures:
12 of {4}*8
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2> of order 12.
12 facets:
12 of {4}*8
12 vertex figures:
12 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2> of order 12.
12 facets:
12 of {4}*8
14 vertex figures:
10 of {4}*8
4 of {2}*4
P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2, s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 12.
12 facets:
12 of {4}*8
14 vertex figures:
10 of {4}*8
4 of {2}*4
P/N, where N=<s1*s2*s1*s2, s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2> of order 12.
12 facets:
12 of {4}*8
14 vertex figures:
4 of {2}*4
10 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 12.
12 facets:
12 of {4}*8
12 vertex figures:
12 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2, s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 12.
12 facets:
12 of {4}*8
12 vertex figures:
12 of {4}*8
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 12.
12 facets:
12 of {4}*8
12 vertex figures:
12 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 12.
12 facets:
12 of {4}*8
12 vertex figures:
12 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 12.
12 facets:
12 of {4}*8
12 vertex figures:
12 of {4}*8
P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 12.
14 facets:
4 of {2}*4
10 of {4}*8
12 vertex figures:
12 of {4}*8
P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s1*s2> of order 12.
14 facets:
4 of {2}*4
10 of {4}*8
12 vertex figures:
12 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2, s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 12.
12 facets:
12 of {4}*8
13 vertex figures:
11 of {4}*8
2 of {2}*4
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 12.
12 facets:
12 of {4}*8
12 vertex figures:
12 of {4}*8
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 12.
12 facets:
12 of {4}*8
12 vertex figures:
12 of {4}*8
P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2> of order 12.
14 facets:
4 of {2}*4
10 of {4}*8
12 vertex figures:
12 of {4}*8
P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 12.
13 facets:
2 of {2}*4
11 of {4}*8
12 vertex figures:
12 of {4}*8
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 24.
6 facets:
6 of {4}*8
6 vertex figures:
6 of {4}*8
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 24.
6 facets:
6 of {4}*8
7 vertex figures:
5 of {4}*8
2 of {2}*4
P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 24.
7 facets:
2 of {2}*4
5 of {4}*8
6 vertex figures:
6 of {4}*8
Permutation Representation (GAP) :
s0 := ( 4, 9)( 5, 7)( 6, 8)( 13, 18)( 14, 16)( 15, 17)( 22, 27)( 23, 25)( 24, 26)( 31, 36)( 32, 34)( 33, 35)( 37, 64)( 38, 65)( 39, 66)( 40, 72)( 41, 70)( 42, 71)( 43, 68)( 44, 69)( 45, 67)( 46, 55)( 47, 56)( 48, 57)( 49, 63)( 50, 61)( 51, 62)( 52, 59)( 53, 60)( 54, 58)( 76, 81)( 77, 79)( 78, 80)( 85, 90)( 86, 88)( 87, 89)( 94, 99)( 95, 97)( 96, 98)(103,108)(104,106)(105,107)(109,136)(110,137)(111,138)(112,144)(113,142)(114,143)(115,140)(116,141)(117,139)(118,127)(119,128)(120,129)(121,135)(122,133)(123,134)(124,131)(125,132)(126,130);;
s1 := ( 2, 6)( 3, 8)( 5, 9)( 11, 15)( 12, 17)( 14, 18)( 19, 28)( 20, 33)( 21, 35)( 22, 31)( 23, 36)( 24, 29)( 25, 34)( 26, 30)( 27, 32)( 38, 42)( 39, 44)( 41, 45)( 47, 51)( 48, 53)( 50, 54)( 55, 64)( 56, 69)( 57, 71)( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 73,109)( 74,114)( 75,116)( 76,112)( 77,117)( 78,110)( 79,115)( 80,111)( 81,113)( 82,118)( 83,123)( 84,125)( 85,121)( 86,126)( 87,119)( 88,124)( 89,120)( 90,122)( 91,136)( 92,141)( 93,143)( 94,139)( 95,144)( 96,137)( 97,142)( 98,138)( 99,140)(100,127)(101,132)(102,134)(103,130)(104,135)(105,128)(106,133)(107,129)(108,131);;
s2 := ( 1, 74)( 2, 73)( 3, 75)( 4, 78)( 5, 77)( 6, 76)( 7, 79)( 8, 81)( 9, 80)( 10, 83)( 11, 82)( 12, 84)( 13, 87)( 14, 86)( 15, 85)( 16, 88)( 17, 90)( 18, 89)( 19, 92)( 20, 91)( 21, 93)( 22, 96)( 23, 95)( 24, 94)( 25, 97)( 26, 99)( 27, 98)( 28,101)( 29,100)( 30,102)( 31,105)( 32,104)( 33,103)( 34,106)( 35,108)( 36,107)( 37,110)( 38,109)( 39,111)( 40,114)( 41,113)( 42,112)( 43,115)( 44,117)( 45,116)( 46,119)( 47,118)( 48,120)( 49,123)( 50,122)( 51,121)( 52,124)( 53,126)( 54,125)( 55,128)( 56,127)( 57,129)( 58,132)( 59,131)( 60,130)( 61,133)( 62,135)( 63,134)( 64,137)( 65,136)( 66,138)( 67,141)( 68,140)( 69,139)( 70,142)( 71,144)( 72,143);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(144)!( 4, 9)( 5, 7)( 6, 8)( 13, 18)( 14, 16)( 15, 17)( 22, 27)( 23, 25)( 24, 26)( 31, 36)( 32, 34)( 33, 35)( 37, 64)( 38, 65)( 39, 66)( 40, 72)( 41, 70)( 42, 71)( 43, 68)( 44, 69)( 45, 67)( 46, 55)( 47, 56)( 48, 57)( 49, 63)( 50, 61)( 51, 62)( 52, 59)( 53, 60)( 54, 58)( 76, 81)( 77, 79)( 78, 80)( 85, 90)( 86, 88)( 87, 89)( 94, 99)( 95, 97)( 96, 98)(103,108)(104,106)(105,107)(109,136)(110,137)(111,138)(112,144)(113,142)(114,143)(115,140)(116,141)(117,139)(118,127)(119,128)(120,129)(121,135)(122,133)(123,134)(124,131)(125,132)(126,130);
s1 := Sym(144)!( 2, 6)( 3, 8)( 5, 9)( 11, 15)( 12, 17)( 14, 18)( 19, 28)( 20, 33)( 21, 35)( 22, 31)( 23, 36)( 24, 29)( 25, 34)( 26, 30)( 27, 32)( 38, 42)( 39, 44)( 41, 45)( 47, 51)( 48, 53)( 50, 54)( 55, 64)( 56, 69)( 57, 71)( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 73,109)( 74,114)( 75,116)( 76,112)( 77,117)( 78,110)( 79,115)( 80,111)( 81,113)( 82,118)( 83,123)( 84,125)( 85,121)( 86,126)( 87,119)( 88,124)( 89,120)( 90,122)( 91,136)( 92,141)( 93,143)( 94,139)( 95,144)( 96,137)( 97,142)( 98,138)( 99,140)(100,127)(101,132)(102,134)(103,130)(104,135)(105,128)(106,133)(107,129)(108,131);
s2 := Sym(144)!( 1, 74)( 2, 73)( 3, 75)( 4, 78)( 5, 77)( 6, 76)( 7, 79)( 8, 81)( 9, 80)( 10, 83)( 11, 82)( 12, 84)( 13, 87)( 14, 86)( 15, 85)( 16, 88)( 17, 90)( 18, 89)( 19, 92)( 20, 91)( 21, 93)( 22, 96)( 23, 95)( 24, 94)( 25, 97)( 26, 99)( 27, 98)( 28,101)( 29,100)( 30,102)( 31,105)( 32,104)( 33,103)( 34,106)( 35,108)( 36,107)( 37,110)( 38,109)( 39,111)( 40,114)( 41,113)( 42,112)( 43,115)( 44,117)( 45,116)( 46,119)( 47,118)( 48,120)( 49,123)( 50,122)( 51,121)( 52,124)( 53,126)( 54,125)( 55,128)( 56,127)( 57,129)( 58,132)( 59,131)( 60,130)( 61,133)( 62,135)( 63,134)( 64,137)( 65,136)( 66,138)( 67,141)( 68,140)( 69,139)( 70,142)( 71,144)( 72,143);
poly := sub<Sym(144)|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, s0*s1*s0*s1*s0*s1*s0*s1,
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;
References : None.
to this polytope
Twisty Puzzle