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# Polytope of Type {4,4}

Atlas Canonical Name : {4,4}*32
Also Known As : {4,4}(2,0), {4,4|2}. if this polytope has another name.
Group : SmallGroup(32,27)
Rank : 3
Schlafli Type : {4,4}
Number of vertices, edges, etc : 4, 8, 4
Order of s0s1s2 : 4
Order of s0s1s2s1 : 2
Special Properties :
Toroidal
Locally Spherical
Orientable
Flat
Self-Dual
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{4,4,2} of size 64
{4,4,4} of size 128
{4,4,6} of size 192
{4,4,3} of size 192
{4,4,8} of size 256
{4,4,8} of size 256
{4,4,4} of size 256
{4,4,6} of size 288
{4,4,10} of size 320
{4,4,12} of size 384
{4,4,6} of size 384
{4,4,14} of size 448
{4,4,5} of size 480
{4,4,8} of size 512
{4,4,16} of size 512
{4,4,16} of size 512
{4,4,4} of size 512
{4,4,8} of size 512
{4,4,18} of size 576
{4,4,9} of size 576
{4,4,4} of size 576
{4,4,6} of size 576
{4,4,20} of size 640
{4,4,22} of size 704
{4,4,24} of size 768
{4,4,24} of size 768
{4,4,12} of size 768
{4,4,6} of size 768
{4,4,12} of size 768
{4,4,12} of size 768
{4,4,10} of size 800
{4,4,26} of size 832
{4,4,6} of size 864
{4,4,28} of size 896
{4,4,30} of size 960
{4,4,6} of size 960
{4,4,5} of size 960
{4,4,10} of size 960
{4,4,10} of size 960
{4,4,15} of size 960
{4,4,34} of size 1088
{4,4,36} of size 1152
{4,4,4} of size 1152
{4,4,12} of size 1152
{4,4,18} of size 1152
{4,4,38} of size 1216
{4,4,40} of size 1280
{4,4,40} of size 1280
{4,4,20} of size 1280
{4,4,5} of size 1280
{4,4,42} of size 1344
{4,4,21} of size 1344
{4,4,44} of size 1408
{4,4,46} of size 1472
{4,4,14} of size 1568
{4,4,50} of size 1600
{4,4,4} of size 1600
{4,4,10} of size 1600
{4,4,52} of size 1664
{4,4,54} of size 1728
{4,4,27} of size 1728
{4,4,12} of size 1728
{4,4,6} of size 1728
{4,4,6} of size 1728
{4,4,12} of size 1728
{4,4,56} of size 1792
{4,4,56} of size 1792
{4,4,28} of size 1792
{4,4,58} of size 1856
{4,4,60} of size 1920
{4,4,30} of size 1920
{4,4,10} of size 1920
{4,4,10} of size 1920
{4,4,10} of size 1920
{4,4,6} of size 1920
{4,4,62} of size 1984
Vertex Figure Of :
{2,4,4} of size 64
{4,4,4} of size 128
{6,4,4} of size 192
{3,4,4} of size 192
{8,4,4} of size 256
{8,4,4} of size 256
{4,4,4} of size 256
{6,4,4} of size 288
{10,4,4} of size 320
{12,4,4} of size 384
{6,4,4} of size 384
{14,4,4} of size 448
{5,4,4} of size 480
{8,4,4} of size 512
{16,4,4} of size 512
{16,4,4} of size 512
{4,4,4} of size 512
{8,4,4} of size 512
{18,4,4} of size 576
{9,4,4} of size 576
{4,4,4} of size 576
{6,4,4} of size 576
{20,4,4} of size 640
{22,4,4} of size 704
{24,4,4} of size 768
{24,4,4} of size 768
{12,4,4} of size 768
{6,4,4} of size 768
{12,4,4} of size 768
{12,4,4} of size 768
{10,4,4} of size 800
{26,4,4} of size 832
{6,4,4} of size 864
{28,4,4} of size 896
{30,4,4} of size 960
{6,4,4} of size 960
{5,4,4} of size 960
{10,4,4} of size 960
{10,4,4} of size 960
{15,4,4} of size 960
{34,4,4} of size 1088
{36,4,4} of size 1152
{4,4,4} of size 1152
{12,4,4} of size 1152
{18,4,4} of size 1152
{38,4,4} of size 1216
{40,4,4} of size 1280
{40,4,4} of size 1280
{20,4,4} of size 1280
{5,4,4} of size 1280
{42,4,4} of size 1344
{21,4,4} of size 1344
{44,4,4} of size 1408
{46,4,4} of size 1472
{14,4,4} of size 1568
{50,4,4} of size 1600
{4,4,4} of size 1600
{10,4,4} of size 1600
{52,4,4} of size 1664
{54,4,4} of size 1728
{27,4,4} of size 1728
{12,4,4} of size 1728
{6,4,4} of size 1728
{6,4,4} of size 1728
{12,4,4} of size 1728
{56,4,4} of size 1792
{56,4,4} of size 1792
{28,4,4} of size 1792
{58,4,4} of size 1856
{60,4,4} of size 1920
{30,4,4} of size 1920
{10,4,4} of size 1920
{10,4,4} of size 1920
{10,4,4} of size 1920
{6,4,4} of size 1920
{62,4,4} of size 1984
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,4}*16, {4,2}*16
4-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,8}*64a, {8,4}*64a, {4,8}*64b, {8,4}*64b, {4,4}*64
3-fold covers : {4,12}*96a, {12,4}*96a
4-fold covers : {4,8}*128a, {8,4}*128a, {8,8}*128a, {8,8}*128b, {8,8}*128c, {8,8}*128d, {4,16}*128a, {16,4}*128a, {4,16}*128b, {16,4}*128b, {4,4}*128, {4,8}*128b, {8,4}*128b
5-fold covers : {4,20}*160, {20,4}*160
6-fold covers : {4,24}*192a, {24,4}*192a, {4,12}*192a, {12,4}*192a, {4,24}*192b, {24,4}*192b, {8,12}*192a, {12,8}*192a, {8,12}*192b, {12,8}*192b
7-fold covers : {4,28}*224, {28,4}*224
8-fold covers : {8,8}*256a, {4,8}*256a, {8,4}*256a, {8,8}*256b, {8,8}*256c, {8,8}*256d, {4,16}*256a, {16,4}*256a, {4,16}*256b, {16,4}*256b, {8,16}*256a, {16,8}*256a, {8,16}*256b, {16,8}*256b, {8,16}*256c, {8,16}*256d, {16,8}*256c, {16,8}*256d, {8,16}*256e, {8,16}*256f, {16,8}*256e, {16,8}*256f, {4,32}*256a, {32,4}*256a, {4,32}*256b, {32,4}*256b, {4,4}*256, {4,8}*256b, {8,4}*256b, {4,8}*256c, {4,8}*256d, {8,4}*256c, {8,4}*256d, {8,8}*256e, {8,8}*256f, {8,8}*256g, {8,8}*256h
9-fold covers : {4,36}*288a, {36,4}*288a, {12,12}*288a, {12,12}*288b, {12,12}*288c, {4,4}*288, {4,12}*288, {12,4}*288
10-fold covers : {4,40}*320a, {40,4}*320a, {4,20}*320, {20,4}*320, {4,40}*320b, {40,4}*320b, {8,20}*320a, {20,8}*320a, {8,20}*320b, {20,8}*320b
11-fold covers : {4,44}*352, {44,4}*352
12-fold covers : {4,24}*384a, {24,4}*384a, {8,24}*384a, {8,24}*384b, {24,8}*384a, {24,8}*384b, {8,12}*384a, {12,8}*384a, {8,24}*384c, {24,8}*384c, {8,24}*384d, {24,8}*384d, {4,48}*384a, {48,4}*384a, {4,48}*384b, {48,4}*384b, {4,12}*384a, {4,24}*384b, {12,4}*384a, {24,4}*384b, {8,12}*384b, {12,8}*384b, {12,16}*384a, {16,12}*384a, {12,16}*384b, {16,12}*384b, {4,12}*384d, {12,4}*384d, {12,12}*384a
13-fold covers : {4,52}*416, {52,4}*416
14-fold covers : {4,56}*448a, {56,4}*448a, {4,28}*448, {28,4}*448, {4,56}*448b, {56,4}*448b, {8,28}*448a, {28,8}*448a, {8,28}*448b, {28,8}*448b
15-fold covers : {12,20}*480, {20,12}*480, {4,60}*480a, {60,4}*480a
16-fold covers : {4,16}*512a, {16,4}*512a, {8,16}*512a, {16,8}*512a, {8,16}*512b, {16,8}*512b, {16,16}*512a, {16,16}*512b, {16,16}*512c, {16,16}*512d, {16,16}*512e, {16,16}*512f, {16,16}*512g, {16,16}*512h, {16,16}*512i, {16,16}*512j, {16,16}*512k, {16,16}*512l, {8,16}*512c, {16,8}*512c, {8,16}*512d, {16,8}*512d, {8,16}*512e, {16,8}*512e, {8,16}*512f, {16,8}*512f, {8,8}*512a, {8,8}*512b, {8,8}*512c, {4,8}*512a, {8,4}*512a, {8,8}*512d, {8,8}*512e, {8,8}*512f, {8,8}*512g, {4,16}*512b, {16,4}*512b, {4,8}*512b, {4,8}*512c, {8,4}*512b, {8,4}*512c, {8,8}*512h, {8,8}*512i, {8,8}*512j, {8,8}*512k, {8,8}*512l, {8,8}*512m, {8,8}*512n, {8,8}*512o, {4,16}*512c, {4,16}*512d, {16,4}*512c, {16,4}*512d, {8,8}*512p, {8,8}*512q, {8,8}*512r, {8,8}*512s, {8,8}*512t, {8,16}*512g, {16,8}*512g, {8,16}*512h, {16,8}*512h, {4,32}*512a, {32,4}*512a, {4,32}*512b, {32,4}*512b, {8,32}*512a, {8,32}*512b, {32,8}*512a, {32,8}*512b, {8,32}*512c, {8,32}*512d, {32,8}*512c, {32,8}*512d, {4,64}*512a, {64,4}*512a, {4,64}*512b, {64,4}*512b, {4,4}*512, {4,16}*512e, {16,4}*512e, {4,8}*512d, {4,16}*512f, {8,4}*512d, {16,4}*512f
17-fold covers : {4,68}*544, {68,4}*544
18-fold covers : {4,72}*576a, {72,4}*576a, {4,36}*576a, {36,4}*576a, {4,72}*576b, {72,4}*576b, {8,36}*576a, {36,8}*576a, {8,36}*576b, {36,8}*576b, {12,24}*576a, {24,12}*576a, {12,12}*576a, {12,12}*576b, {12,12}*576c, {12,24}*576b, {24,12}*576b, {12,24}*576c, {12,24}*576d, {24,12}*576c, {24,12}*576d, {12,24}*576e, {12,24}*576f, {24,12}*576e, {24,12}*576f, {4,4}*576, {4,12}*576, {12,4}*576, {8,12}*576a, {12,8}*576a, {4,8}*576a, {4,24}*576a, {8,4}*576a, {24,4}*576a, {4,8}*576b, {4,24}*576b, {8,4}*576b, {24,4}*576b, {8,12}*576b, {12,8}*576b
19-fold covers : {4,76}*608, {76,4}*608
20-fold covers : {4,40}*640a, {40,4}*640a, {8,40}*640a, {8,40}*640b, {40,8}*640a, {40,8}*640b, {8,20}*640a, {20,8}*640a, {8,40}*640c, {40,8}*640c, {8,40}*640d, {40,8}*640d, {4,80}*640a, {80,4}*640a, {4,80}*640b, {80,4}*640b, {4,20}*640a, {4,40}*640b, {20,4}*640a, {40,4}*640b, {8,20}*640b, {20,8}*640b, {16,20}*640a, {20,16}*640a, {16,20}*640b, {20,16}*640b
21-fold covers : {12,28}*672, {28,12}*672, {4,84}*672a, {84,4}*672a
22-fold covers : {4,88}*704a, {88,4}*704a, {4,44}*704, {44,4}*704, {4,88}*704b, {88,4}*704b, {8,44}*704a, {44,8}*704a, {8,44}*704b, {44,8}*704b
23-fold covers : {4,92}*736, {92,4}*736
24-fold covers : {8,24}*768a, {24,8}*768a, {8,12}*768a, {8,24}*768b, {12,8}*768a, {24,8}*768b, {4,24}*768a, {24,4}*768a, {8,24}*768c, {24,8}*768c, {8,24}*768d, {24,8}*768d, {12,16}*768a, {16,12}*768a, {4,48}*768a, {48,4}*768a, {12,16}*768b, {16,12}*768b, {4,48}*768b, {48,4}*768b, {8,48}*768a, {48,8}*768a, {16,24}*768a, {24,16}*768a, {8,48}*768b, {48,8}*768b, {16,24}*768b, {24,16}*768b, {16,24}*768c, {24,16}*768c, {8,48}*768c, {8,48}*768d, {48,8}*768c, {48,8}*768d, {16,24}*768d, {24,16}*768d, {16,24}*768e, {24,16}*768e, {8,48}*768e, {8,48}*768f, {48,8}*768e, {48,8}*768f, {16,24}*768f, {24,16}*768f, {12,32}*768a, {32,12}*768a, {4,96}*768a, {96,4}*768a, {12,32}*768b, {32,12}*768b, {4,96}*768b, {96,4}*768b, {4,12}*768a, {4,24}*768b, {12,4}*768a, {24,4}*768b, {8,12}*768b, {12,8}*768b, {8,12}*768c, {8,24}*768e, {12,8}*768c, {24,8}*768e, {4,24}*768c, {4,24}*768d, {24,4}*768c, {24,4}*768d, {8,12}*768d, {8,24}*768f, {12,8}*768d, {24,8}*768f, {8,24}*768g, {24,8}*768g, {8,24}*768h, {24,8}*768h, {8,12}*768s, {12,8}*768s, {12,12}*768a, {4,24}*768i, {24,4}*768i, {4,12}*768d, {12,4}*768d, {12,12}*768b, {8,12}*768t, {12,8}*768t, {12,12}*768c, {4,24}*768j, {24,4}*768j, {8,12}*768u, {12,8}*768u, {12,24}*768c, {24,12}*768c, {4,12}*768e, {4,24}*768k, {12,4}*768e, {12,24}*768d, {24,4}*768k, {24,12}*768d, {8,12}*768w, {12,8}*768w, {12,24}*768e, {24,12}*768e, {4,12}*768f, {4,24}*768l, {12,4}*768f, {12,24}*768f, {24,4}*768l, {24,12}*768f
25-fold covers : {4,100}*800, {100,4}*800, {20,20}*800a, {20,20}*800b, {20,20}*800c, {4,4}*800, {4,20}*800, {20,4}*800
26-fold covers : {4,104}*832a, {104,4}*832a, {4,52}*832, {52,4}*832, {4,104}*832b, {104,4}*832b, {8,52}*832a, {52,8}*832a, {8,52}*832b, {52,8}*832b
27-fold covers : {4,108}*864a, {108,4}*864a, {12,36}*864a, {12,36}*864b, {36,12}*864a, {36,12}*864b, {12,12}*864a, {12,12}*864b, {12,12}*864c, {4,12}*864a, {4,12}*864b, {12,4}*864a, {12,4}*864b, {12,12}*864d, {12,12}*864e, {12,12}*864f, {12,12}*864g, {12,12}*864h, {4,12}*864c, {4,12}*864d, {12,4}*864c, {12,4}*864d, {12,12}*864i, {12,12}*864j, {12,12}*864k, {12,12}*864l
28-fold covers : {4,56}*896a, {56,4}*896a, {8,56}*896a, {8,56}*896b, {56,8}*896a, {56,8}*896b, {8,28}*896a, {28,8}*896a, {8,56}*896c, {56,8}*896c, {8,56}*896d, {56,8}*896d, {4,112}*896a, {112,4}*896a, {4,112}*896b, {112,4}*896b, {4,28}*896, {4,56}*896b, {28,4}*896, {56,4}*896b, {8,28}*896b, {28,8}*896b, {16,28}*896a, {28,16}*896a, {16,28}*896b, {28,16}*896b
29-fold covers : {4,116}*928, {116,4}*928
30-fold covers : {12,20}*960a, {20,12}*960a, {20,24}*960a, {24,20}*960a, {12,40}*960a, {40,12}*960a, {20,24}*960b, {24,20}*960b, {12,40}*960b, {40,12}*960b, {4,120}*960a, {120,4}*960a, {4,60}*960a, {60,4}*960a, {4,120}*960b, {120,4}*960b, {8,60}*960a, {60,8}*960a, {8,60}*960b, {60,8}*960b
31-fold covers : {4,124}*992, {124,4}*992
33-fold covers : {12,44}*1056, {44,12}*1056, {4,132}*1056a, {132,4}*1056a
34-fold covers : {8,68}*1088a, {68,8}*1088a, {4,136}*1088a, {136,4}*1088a, {8,68}*1088b, {68,8}*1088b, {4,136}*1088b, {136,4}*1088b, {4,68}*1088, {68,4}*1088
35-fold covers : {20,28}*1120, {28,20}*1120, {4,140}*1120, {140,4}*1120
36-fold covers : {8,36}*1152a, {36,8}*1152a, {4,72}*1152a, {72,4}*1152a, {12,24}*1152a, {12,24}*1152b, {24,12}*1152a, {24,12}*1152b, {12,24}*1152c, {24,12}*1152c, {4,8}*1152a, {4,24}*1152a, {8,4}*1152a, {24,4}*1152a, {8,12}*1152a, {12,8}*1152a, {8,72}*1152a, {72,8}*1152a, {8,72}*1152b, {8,72}*1152c, {72,8}*1152b, {72,8}*1152c, {24,24}*1152a, {24,24}*1152b, {24,24}*1152c, {24,24}*1152d, {24,24}*1152e, {24,24}*1152f, {24,24}*1152g, {24,24}*1152h, {24,24}*1152i, {8,8}*1152a, {8,24}*1152a, {24,8}*1152a, {8,8}*1152b, {8,8}*1152c, {8,24}*1152b, {8,24}*1152c, {24,8}*1152b, {24,8}*1152c, {8,72}*1152d, {72,8}*1152d, {24,24}*1152j, {24,24}*1152k, {24,24}*1152l, {8,8}*1152d, {8,24}*1152d, {24,8}*1152d, {16,36}*1152a, {36,16}*1152a, {4,144}*1152a, {144,4}*1152a, {12,48}*1152a, {12,48}*1152b, {48,12}*1152a, {48,12}*1152b, {12,48}*1152c, {48,12}*1152c, {4,16}*1152a, {4,48}*1152a, {16,4}*1152a, {48,4}*1152a, {12,16}*1152a, {16,12}*1152a, {16,36}*1152b, {36,16}*1152b, {4,144}*1152b, {144,4}*1152b, {12,48}*1152d, {12,48}*1152e, {48,12}*1152d, {48,12}*1152e, {12,48}*1152f, {48,12}*1152f, {4,16}*1152b, {4,48}*1152b, {16,4}*1152b, {48,4}*1152b, {12,16}*1152b, {16,12}*1152b, {4,36}*1152a, {4,72}*1152b, {36,4}*1152a, {72,4}*1152b, {8,36}*1152b, {36,8}*1152b, {12,12}*1152a, {12,12}*1152b, {12,24}*1152d, {12,24}*1152e, {24,12}*1152d, {24,12}*1152e, {12,12}*1152c, {12,24}*1152f, {24,12}*1152f, {4,8}*1152b, {4,12}*1152a, {8,4}*1152b, {8,12}*1152b, {12,4}*1152a, {12,8}*1152b, {4,4}*1152, {4,24}*1152b, {24,4}*1152b, {4,36}*1152d, {36,4}*1152d, {12,12}*1152j, {12,12}*1152k, {12,12}*1152l, {12,12}*1152m, {12,12}*1152n, {12,12}*1152o
37-fold covers : {4,148}*1184, {148,4}*1184
38-fold covers : {8,76}*1216a, {76,8}*1216a, {4,152}*1216a, {152,4}*1216a, {8,76}*1216b, {76,8}*1216b, {4,152}*1216b, {152,4}*1216b, {4,76}*1216, {76,4}*1216
39-fold covers : {12,52}*1248, {52,12}*1248, {4,156}*1248a, {156,4}*1248a
40-fold covers : {8,40}*1280a, {40,8}*1280a, {8,20}*1280a, {8,40}*1280b, {20,8}*1280a, {40,8}*1280b, {4,40}*1280a, {40,4}*1280a, {8,40}*1280c, {40,8}*1280c, {8,40}*1280d, {40,8}*1280d, {16,20}*1280a, {20,16}*1280a, {4,80}*1280a, {80,4}*1280a, {16,20}*1280b, {20,16}*1280b, {4,80}*1280b, {80,4}*1280b, {8,80}*1280a, {80,8}*1280a, {16,40}*1280a, {40,16}*1280a, {8,80}*1280b, {80,8}*1280b, {16,40}*1280b, {40,16}*1280b, {16,40}*1280c, {40,16}*1280c, {8,80}*1280c, {8,80}*1280d, {80,8}*1280c, {80,8}*1280d, {16,40}*1280d, {40,16}*1280d, {16,40}*1280e, {40,16}*1280e, {8,80}*1280e, {8,80}*1280f, {80,8}*1280e, {80,8}*1280f, {16,40}*1280f, {40,16}*1280f, {20,32}*1280a, {32,20}*1280a, {4,160}*1280a, {160,4}*1280a, {20,32}*1280b, {32,20}*1280b, {4,160}*1280b, {160,4}*1280b, {4,20}*1280a, {4,40}*1280b, {20,4}*1280a, {40,4}*1280b, {8,20}*1280b, {20,8}*1280b, {8,20}*1280c, {8,40}*1280e, {20,8}*1280c, {40,8}*1280e, {4,40}*1280c, {4,40}*1280d, {40,4}*1280c, {40,4}*1280d, {8,20}*1280d, {8,40}*1280f, {20,8}*1280d, {40,8}*1280f, {8,40}*1280g, {40,8}*1280g, {8,40}*1280h, {40,8}*1280h
41-fold covers : {4,164}*1312, {164,4}*1312
42-fold covers : {12,28}*1344a, {28,12}*1344a, {24,28}*1344a, {28,24}*1344a, {12,56}*1344a, {56,12}*1344a, {24,28}*1344b, {28,24}*1344b, {12,56}*1344b, {56,12}*1344b, {4,168}*1344a, {168,4}*1344a, {4,84}*1344a, {84,4}*1344a, {4,168}*1344b, {168,4}*1344b, {8,84}*1344a, {84,8}*1344a, {8,84}*1344b, {84,8}*1344b
43-fold covers : {4,172}*1376, {172,4}*1376
44-fold covers : {8,44}*1408a, {44,8}*1408a, {4,88}*1408a, {88,4}*1408a, {8,88}*1408a, {88,8}*1408a, {8,88}*1408b, {8,88}*1408c, {88,8}*1408b, {88,8}*1408c, {8,88}*1408d, {88,8}*1408d, {16,44}*1408a, {44,16}*1408a, {4,176}*1408a, {176,4}*1408a, {16,44}*1408b, {44,16}*1408b, {4,176}*1408b, {176,4}*1408b, {4,44}*1408, {4,88}*1408b, {44,4}*1408, {88,4}*1408b, {8,44}*1408b, {44,8}*1408b
45-fold covers : {20,36}*1440, {36,20}*1440, {4,180}*1440a, {180,4}*1440a, {12,60}*1440a, {60,12}*1440a, {12,60}*1440b, {12,60}*1440c, {60,12}*1440b, {60,12}*1440c, {4,20}*1440, {4,60}*1440, {20,4}*1440, {60,4}*1440, {12,20}*1440, {20,12}*1440
46-fold covers : {8,92}*1472a, {92,8}*1472a, {4,184}*1472a, {184,4}*1472a, {8,92}*1472b, {92,8}*1472b, {4,184}*1472b, {184,4}*1472b, {4,92}*1472, {92,4}*1472
47-fold covers : {4,188}*1504, {188,4}*1504
49-fold covers : {4,196}*1568, {196,4}*1568, {28,28}*1568a, {28,28}*1568b, {28,28}*1568c, {4,4}*1568, {4,28}*1568, {28,4}*1568
50-fold covers : {4,200}*1600a, {200,4}*1600a, {4,100}*1600, {100,4}*1600, {4,200}*1600b, {200,4}*1600b, {8,100}*1600a, {100,8}*1600a, {8,100}*1600b, {100,8}*1600b, {20,40}*1600a, {40,20}*1600a, {20,20}*1600a, {20,20}*1600b, {20,20}*1600c, {20,40}*1600b, {40,20}*1600b, {20,40}*1600c, {20,40}*1600d, {40,20}*1600c, {40,20}*1600d, {20,40}*1600e, {20,40}*1600f, {40,20}*1600e, {40,20}*1600f, {4,4}*1600, {4,20}*1600, {20,4}*1600, {8,20}*1600a, {20,8}*1600a, {4,8}*1600a, {4,40}*1600a, {8,4}*1600a, {40,4}*1600a, {4,8}*1600b, {4,40}*1600b, {8,4}*1600b, {40,4}*1600b, {8,20}*1600b, {20,8}*1600b
51-fold covers : {12,68}*1632, {68,12}*1632, {4,204}*1632a, {204,4}*1632a
52-fold covers : {8,52}*1664a, {52,8}*1664a, {4,104}*1664a, {104,4}*1664a, {8,104}*1664a, {104,8}*1664a, {8,104}*1664b, {8,104}*1664c, {104,8}*1664b, {104,8}*1664c, {8,104}*1664d, {104,8}*1664d, {16,52}*1664a, {52,16}*1664a, {4,208}*1664a, {208,4}*1664a, {16,52}*1664b, {52,16}*1664b, {4,208}*1664b, {208,4}*1664b, {4,52}*1664, {4,104}*1664b, {52,4}*1664, {104,4}*1664b, {8,52}*1664b, {52,8}*1664b
53-fold covers : {4,212}*1696, {212,4}*1696
54-fold covers : {4,216}*1728a, {216,4}*1728a, {4,108}*1728a, {108,4}*1728a, {4,216}*1728b, {216,4}*1728b, {8,108}*1728a, {108,8}*1728a, {8,108}*1728b, {108,8}*1728b, {24,36}*1728a, {36,24}*1728a, {12,24}*1728a, {24,12}*1728a, {12,36}*1728a, {12,36}*1728b, {36,12}*1728a, {36,12}*1728b, {12,12}*1728a, {12,12}*1728b, {12,12}*1728c, {24,36}*1728b, {36,24}*1728b, {12,24}*1728b, {24,12}*1728b, {12,72}*1728a, {12,72}*1728b, {72,12}*1728a, {72,12}*1728b, {24,36}*1728c, {36,24}*1728c, {12,24}*1728c, {12,24}*1728d, {24,12}*1728c, {24,12}*1728d, {12,72}*1728c, {12,72}*1728d, {72,12}*1728c, {72,12}*1728d, {24,36}*1728d, {36,24}*1728d, {12,24}*1728e, {12,24}*1728f, {24,12}*1728e, {24,12}*1728f, {4,12}*1728a, {4,12}*1728b, {12,4}*1728a, {12,4}*1728b, {12,12}*1728d, {12,12}*1728e, {12,12}*1728f, {12,12}*1728g, {8,12}*1728a, {12,8}*1728a, {12,24}*1728g, {12,24}*1728h, {24,12}*1728g, {24,12}*1728h, {4,24}*1728a, {4,24}*1728b, {8,12}*1728b, {12,8}*1728b, {12,24}*1728i, {12,24}*1728j, {24,4}*1728a, {24,4}*1728b, {24,12}*1728i, {24,12}*1728j, {4,24}*1728c, {4,24}*1728d, {8,12}*1728c, {12,8}*1728c, {12,24}*1728k, {12,24}*1728l, {24,4}*1728c, {24,4}*1728d, {24,12}*1728k, {24,12}*1728l, {8,12}*1728d, {12,8}*1728d, {12,24}*1728m, {12,24}*1728n, {24,12}*1728m, {24,12}*1728n, {12,24}*1728o, {24,12}*1728o, {12,24}*1728p, {24,12}*1728p, {12,12}*1728h, {4,24}*1728e, {4,24}*1728f, {24,4}*1728e, {24,4}*1728f, {8,12}*1728e, {12,8}*1728e, {12,24}*1728q, {24,12}*1728q, {4,24}*1728g, {4,24}*1728h, {24,4}*1728g, {24,4}*1728h, {8,12}*1728f, {12,8}*1728f, {12,24}*1728r, {24,12}*1728r, {8,12}*1728g, {12,8}*1728g, {12,24}*1728s, {24,12}*1728s, {8,12}*1728h, {12,8}*1728h, {12,24}*1728t, {24,12}*1728t, {4,12}*1728c, {4,12}*1728d, {12,4}*1728c, {12,4}*1728d, {12,12}*1728q, {12,12}*1728r, {12,12}*1728s, {12,12}*1728t, {12,24}*1728u, {24,12}*1728u, {12,24}*1728v, {24,12}*1728v, {12,24}*1728w, {24,12}*1728w, {12,24}*1728x, {24,12}*1728x
55-fold covers : {20,44}*1760, {44,20}*1760, {4,220}*1760, {220,4}*1760
56-fold covers : {8,56}*1792a, {56,8}*1792a, {8,28}*1792a, {8,56}*1792b, {28,8}*1792a, {56,8}*1792b, {4,56}*1792a, {56,4}*1792a, {8,56}*1792c, {56,8}*1792c, {8,56}*1792d, {56,8}*1792d, {16,28}*1792a, {28,16}*1792a, {4,112}*1792a, {112,4}*1792a, {16,28}*1792b, {28,16}*1792b, {4,112}*1792b, {112,4}*1792b, {8,112}*1792a, {112,8}*1792a, {16,56}*1792a, {56,16}*1792a, {8,112}*1792b, {112,8}*1792b, {16,56}*1792b, {56,16}*1792b, {16,56}*1792c, {56,16}*1792c, {8,112}*1792c, {8,112}*1792d, {112,8}*1792c, {112,8}*1792d, {16,56}*1792d, {56,16}*1792d, {16,56}*1792e, {56,16}*1792e, {8,112}*1792e, {8,112}*1792f, {112,8}*1792e, {112,8}*1792f, {16,56}*1792f, {56,16}*1792f, {28,32}*1792a, {32,28}*1792a, {4,224}*1792a, {224,4}*1792a, {28,32}*1792b, {32,28}*1792b, {4,224}*1792b, {224,4}*1792b, {4,28}*1792, {4,56}*1792b, {28,4}*1792, {56,4}*1792b, {8,28}*1792b, {28,8}*1792b, {8,28}*1792c, {8,56}*1792e, {28,8}*1792c, {56,8}*1792e, {4,56}*1792c, {4,56}*1792d, {56,4}*1792c, {56,4}*1792d, {8,28}*1792d, {8,56}*1792f, {28,8}*1792d, {56,8}*1792f, {8,56}*1792g, {56,8}*1792g, {8,56}*1792h, {56,8}*1792h
57-fold covers : {12,76}*1824, {76,12}*1824, {4,228}*1824a, {228,4}*1824a
58-fold covers : {8,116}*1856a, {116,8}*1856a, {4,232}*1856a, {232,4}*1856a, {8,116}*1856b, {116,8}*1856b, {4,232}*1856b, {232,4}*1856b, {4,116}*1856, {116,4}*1856
59-fold covers : {4,236}*1888, {236,4}*1888
60-fold covers : {8,60}*1920a, {60,8}*1920a, {4,120}*1920a, {120,4}*1920a, {12,40}*1920a, {40,12}*1920a, {20,24}*1920a, {24,20}*1920a, {8,120}*1920a, {120,8}*1920a, {8,120}*1920b, {8,120}*1920c, {120,8}*1920b, {120,8}*1920c, {24,40}*1920a, {40,24}*1920a, {24,40}*1920b, {40,24}*1920b, {24,40}*1920c, {40,24}*1920c, {8,120}*1920d, {120,8}*1920d, {24,40}*1920d, {40,24}*1920d, {16,60}*1920a, {60,16}*1920a, {4,240}*1920a, {240,4}*1920a, {12,80}*1920a, {80,12}*1920a, {20,48}*1920a, {48,20}*1920a, {16,60}*1920b, {60,16}*1920b, {4,240}*1920b, {240,4}*1920b, {12,80}*1920b, {80,12}*1920b, {20,48}*1920b, {48,20}*1920b, {4,60}*1920a, {4,120}*1920b, {60,4}*1920a, {120,4}*1920b, {8,60}*1920b, {60,8}*1920b, {12,40}*1920b, {40,12}*1920b, {20,24}*1920b, {24,20}*1920b, {12,20}*1920a, {20,12}*1920a, {12,20}*1920c, {12,60}*1920c, {20,12}*1920c, {60,12}*1920c, {4,60}*1920d, {60,4}*1920d, {4,12}*1920a, {4,20}*1920a, {12,4}*1920a, {12,20}*1920f, {20,4}*1920a, {20,12}*1920f, {12,12}*1920a, {12,20}*1920g, {20,12}*1920g, {20,20}*1920a
61-fold covers : {4,244}*1952, {244,4}*1952
62-fold covers : {8,124}*1984a, {124,8}*1984a, {4,248}*1984a, {248,4}*1984a, {8,124}*1984b, {124,8}*1984b, {4,248}*1984b, {248,4}*1984b, {4,124}*1984, {124,4}*1984
Permutation Representation (GAP) :
```s0 := (2,3)(4,6);;
s1 := (1,2)(3,5)(4,7)(6,8);;
s2 := (2,4)(3,6);;
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,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(8)!(2,3)(4,6);
s1 := Sym(8)!(1,2)(3,5)(4,7)(6,8);
s2 := Sym(8)!(2,4)(3,6);
poly := sub<Sym(8)|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,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2 >;

```
References : None.
to this polytope