Polytope of Type {4,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,2}*32
if this polytope has a name.
Group : SmallGroup(32,46)
Rank : 4
Schlafli Type : {4,2,2}
Number of vertices, edges, etc : 4, 4, 2, 2
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,2,2,2} of size 64
{4,2,2,3} of size 96
{4,2,2,4} of size 128
{4,2,2,5} of size 160
{4,2,2,6} of size 192
{4,2,2,7} of size 224
{4,2,2,8} of size 256
{4,2,2,9} of size 288
{4,2,2,10} of size 320
{4,2,2,11} of size 352
{4,2,2,12} of size 384
{4,2,2,13} of size 416
{4,2,2,14} of size 448
{4,2,2,15} of size 480
{4,2,2,16} of size 512
{4,2,2,17} of size 544
{4,2,2,18} of size 576
{4,2,2,19} of size 608
{4,2,2,20} of size 640
{4,2,2,21} of size 672
{4,2,2,22} of size 704
{4,2,2,23} of size 736
{4,2,2,24} of size 768
{4,2,2,25} of size 800
{4,2,2,26} of size 832
{4,2,2,27} of size 864
{4,2,2,28} of size 896
{4,2,2,29} of size 928
{4,2,2,30} of size 960
{4,2,2,31} of size 992
{4,2,2,33} of size 1056
{4,2,2,34} of size 1088
{4,2,2,35} of size 1120
{4,2,2,36} of size 1152
{4,2,2,37} of size 1184
{4,2,2,38} of size 1216
{4,2,2,39} of size 1248
{4,2,2,40} of size 1280
{4,2,2,41} of size 1312
{4,2,2,42} of size 1344
{4,2,2,43} of size 1376
{4,2,2,44} of size 1408
{4,2,2,45} of size 1440
{4,2,2,46} of size 1472
{4,2,2,47} of size 1504
{4,2,2,49} of size 1568
{4,2,2,50} of size 1600
{4,2,2,51} of size 1632
{4,2,2,52} of size 1664
{4,2,2,53} of size 1696
{4,2,2,54} of size 1728
{4,2,2,55} of size 1760
{4,2,2,56} of size 1792
{4,2,2,57} of size 1824
{4,2,2,58} of size 1856
{4,2,2,59} of size 1888
{4,2,2,60} of size 1920
{4,2,2,61} of size 1952
{4,2,2,62} of size 1984
Vertex Figure Of :
{2,4,2,2} of size 64
{3,4,2,2} of size 96
{4,4,2,2} of size 128
{6,4,2,2} of size 192
{3,4,2,2} of size 192
{6,4,2,2} of size 192
{6,4,2,2} of size 192
{8,4,2,2} of size 256
{8,4,2,2} of size 256
{4,4,2,2} of size 256
{9,4,2,2} of size 288
{4,4,2,2} of size 288
{6,4,2,2} of size 288
{10,4,2,2} of size 320
{12,4,2,2} of size 384
{12,4,2,2} of size 384
{12,4,2,2} of size 384
{6,4,2,2} of size 384
{14,4,2,2} of size 448
{5,4,2,2} of size 480
{6,4,2,2} of size 480
{15,4,2,2} of size 480
{8,4,2,2} of size 512
{16,4,2,2} of size 512
{16,4,2,2} of size 512
{4,4,2,2} of size 512
{8,4,2,2} of size 512
{18,4,2,2} of size 576
{9,4,2,2} of size 576
{18,4,2,2} of size 576
{18,4,2,2} of size 576
{4,4,2,2} of size 576
{6,4,2,2} of size 576
{20,4,2,2} of size 640
{5,4,2,2} of size 640
{21,4,2,2} of size 672
{22,4,2,2} of size 704
{24,4,2,2} of size 768
{24,4,2,2} of size 768
{12,4,2,2} of size 768
{6,4,2,2} of size 768
{24,4,2,2} of size 768
{24,4,2,2} of size 768
{12,4,2,2} of size 768
{6,4,2,2} of size 768
{12,4,2,2} of size 768
{4,4,2,2} of size 800
{10,4,2,2} of size 800
{26,4,2,2} of size 832
{27,4,2,2} of size 864
{6,4,2,2} of size 864
{12,4,2,2} of size 864
{28,4,2,2} of size 896
{30,4,2,2} of size 960
{5,4,2,2} of size 960
{6,4,2,2} of size 960
{6,4,2,2} of size 960
{6,4,2,2} of size 960
{10,4,2,2} of size 960
{10,4,2,2} of size 960
{15,4,2,2} of size 960
{30,4,2,2} of size 960
{30,4,2,2} of size 960
{33,4,2,2} of size 1056
{34,4,2,2} of size 1088
{36,4,2,2} of size 1152
{4,4,2,2} of size 1152
{12,4,2,2} of size 1152
{36,4,2,2} of size 1152
{36,4,2,2} of size 1152
{18,4,2,2} of size 1152
{38,4,2,2} of size 1216
{39,4,2,2} of size 1248
{40,4,2,2} of size 1280
{40,4,2,2} of size 1280
{20,4,2,2} of size 1280
{5,4,2,2} of size 1280
{10,4,2,2} of size 1280
{10,4,2,2} of size 1280
{42,4,2,2} of size 1344
{6,4,2,2} of size 1344
{7,4,2,2} of size 1344
{8,4,2,2} of size 1344
{8,4,2,2} of size 1344
{21,4,2,2} of size 1344
{42,4,2,2} of size 1344
{42,4,2,2} of size 1344
{44,4,2,2} of size 1408
{45,4,2,2} of size 1440
{46,4,2,2} of size 1472
{4,4,2,2} of size 1568
{14,4,2,2} of size 1568
{50,4,2,2} of size 1600
{4,4,2,2} of size 1600
{10,4,2,2} of size 1600
{51,4,2,2} of size 1632
{52,4,2,2} of size 1664
{54,4,2,2} of size 1728
{27,4,2,2} of size 1728
{54,4,2,2} of size 1728
{54,4,2,2} of size 1728
{6,4,2,2} of size 1728
{12,4,2,2} of size 1728
{6,4,2,2} of size 1728
{12,4,2,2} of size 1728
{56,4,2,2} of size 1792
{56,4,2,2} of size 1792
{28,4,2,2} of size 1792
{57,4,2,2} of size 1824
{58,4,2,2} of size 1856
{60,4,2,2} of size 1920
{60,4,2,2} of size 1920
{60,4,2,2} of size 1920
{15,4,2,2} of size 1920
{30,4,2,2} of size 1920
{10,4,2,2} of size 1920
{10,4,2,2} of size 1920
{12,4,2,2} of size 1920
{12,4,2,2} of size 1920
{6,4,2,2} of size 1920
{10,4,2,2} of size 1920
{62,4,2,2} of size 1984
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,4,2}*64, {4,2,4}*64, {8,2,2}*64
3-fold covers : {12,2,2}*96, {4,2,6}*96, {4,6,2}*96a
4-fold covers : {4,4,4}*128, {4,8,2}*128a, {8,4,2}*128a, {4,8,2}*128b, {8,4,2}*128b, {4,4,2}*128, {4,2,8}*128, {8,2,4}*128, {16,2,2}*128
5-fold covers : {20,2,2}*160, {4,2,10}*160, {4,10,2}*160
6-fold covers : {4,12,2}*192a, {12,4,2}*192a, {4,2,12}*192, {12,2,4}*192, {4,4,6}*192, {4,6,4}*192a, {24,2,2}*192, {8,2,6}*192, {8,6,2}*192
7-fold covers : {28,2,2}*224, {4,2,14}*224, {4,14,2}*224
8-fold covers : {4,8,2}*256a, {8,4,2}*256a, {8,8,2}*256a, {8,8,2}*256b, {8,8,2}*256c, {8,8,2}*256d, {8,2,8}*256, {4,4,8}*256a, {8,4,4}*256a, {4,4,8}*256b, {8,4,4}*256b, {4,8,4}*256a, {4,4,4}*256a, {4,4,4}*256b, {4,8,4}*256b, {4,8,4}*256c, {4,8,4}*256d, {4,16,2}*256a, {16,4,2}*256a, {4,16,2}*256b, {16,4,2}*256b, {4,4,2}*256, {4,8,2}*256b, {8,4,2}*256b, {4,2,16}*256, {16,2,4}*256, {32,2,2}*256
9-fold covers : {36,2,2}*288, {4,2,18}*288, {4,18,2}*288a, {12,2,6}*288, {12,6,2}*288a, {12,6,2}*288b, {4,6,6}*288a, {4,6,6}*288b, {4,6,6}*288c, {12,6,2}*288c, {4,6,2}*288
10-fold covers : {4,20,2}*320, {20,4,2}*320, {4,2,20}*320, {20,2,4}*320, {4,4,10}*320, {4,10,4}*320, {40,2,2}*320, {8,2,10}*320, {8,10,2}*320
11-fold covers : {44,2,2}*352, {4,2,22}*352, {4,22,2}*352
12-fold covers : {4,12,4}*384a, {4,4,12}*384, {12,4,4}*384, {4,24,2}*384a, {24,4,2}*384a, {4,12,2}*384a, {12,4,2}*384a, {4,24,2}*384b, {24,4,2}*384b, {8,12,2}*384a, {12,8,2}*384a, {8,12,2}*384b, {12,8,2}*384b, {4,2,24}*384, {24,2,4}*384, {8,2,12}*384, {12,2,8}*384, {4,8,6}*384a, {8,4,6}*384a, {4,6,8}*384a, {8,6,4}*384a, {4,8,6}*384b, {8,4,6}*384b, {4,4,6}*384a, {48,2,2}*384, {16,2,6}*384, {16,6,2}*384, {12,4,2}*384b, {4,4,6}*384d, {4,6,4}*384a, {4,6,6}*384, {4,6,2}*384b, {12,6,2}*384a
13-fold covers : {52,2,2}*416, {4,2,26}*416, {4,26,2}*416
14-fold covers : {4,28,2}*448, {28,4,2}*448, {4,2,28}*448, {28,2,4}*448, {4,4,14}*448, {4,14,4}*448, {56,2,2}*448, {8,2,14}*448, {8,14,2}*448
15-fold covers : {12,2,10}*480, {12,10,2}*480, {20,2,6}*480, {20,6,2}*480a, {4,6,10}*480a, {4,10,6}*480, {60,2,2}*480, {4,2,30}*480, {4,30,2}*480a
16-fold covers : {8,8,2}*512a, {8,4,8}*512a, {8,4,8}*512b, {4,4,4}*512a, {4,8,8}*512a, {8,8,4}*512a, {4,8,8}*512b, {8,8,4}*512b, {4,4,8}*512a, {8,4,4}*512a, {4,8,8}*512c, {8,8,4}*512c, {4,8,8}*512d, {8,8,4}*512d, {4,8,8}*512e, {4,8,8}*512f, {8,8,4}*512e, {8,8,4}*512f, {4,8,8}*512g, {8,8,4}*512g, {4,8,8}*512h, {8,8,4}*512h, {4,4,8}*512b, {8,4,4}*512b, {4,4,8}*512c, {8,4,4}*512c, {4,8,4}*512a, {4,8,4}*512b, {4,8,4}*512c, {4,8,4}*512d, {8,4,8}*512c, {8,4,8}*512d, {4,8,2}*512a, {8,4,2}*512a, {8,8,2}*512b, {8,8,2}*512c, {8,8,2}*512d, {4,16,2}*512a, {16,4,2}*512a, {4,16,2}*512b, {16,4,2}*512b, {8,16,2}*512a, {16,8,2}*512a, {8,16,2}*512b, {16,8,2}*512b, {8,16,2}*512c, {8,16,2}*512d, {16,8,2}*512c, {16,8,2}*512d, {8,16,2}*512e, {8,16,2}*512f, {16,8,2}*512e, {16,8,2}*512f, {4,4,16}*512a, {16,4,4}*512a, {4,4,16}*512b, {16,4,4}*512b, {4,4,4}*512b, {4,4,4}*512c, {4,8,4}*512e, {4,8,4}*512f, {4,8,4}*512g, {4,8,4}*512h, {4,4,8}*512d, {8,4,4}*512d, {4,16,4}*512a, {4,16,4}*512b, {4,16,4}*512c, {4,16,4}*512d, {4,32,2}*512a, {32,4,2}*512a, {4,32,2}*512b, {32,4,2}*512b, {4,4,2}*512, {4,8,2}*512b, {8,4,2}*512b, {4,8,2}*512c, {4,8,2}*512d, {8,4,2}*512c, {8,4,2}*512d, {8,8,2}*512e, {8,8,2}*512f, {8,8,2}*512g, {8,8,2}*512h, {64,2,2}*512
17-fold covers : {68,2,2}*544, {4,2,34}*544, {4,34,2}*544
18-fold covers : {4,36,2}*576a, {36,4,2}*576a, {4,2,36}*576, {36,2,4}*576, {4,4,18}*576, {4,18,4}*576a, {72,2,2}*576, {8,2,18}*576, {8,18,2}*576, {12,2,12}*576, {4,12,6}*576a, {4,12,6}*576b, {12,4,6}*576, {4,6,12}*576a, {12,6,4}*576a, {24,2,6}*576, {24,6,2}*576a, {24,6,2}*576b, {8,6,6}*576a, {8,6,6}*576b, {12,12,2}*576a, {12,12,2}*576b, {12,12,2}*576c, {4,6,12}*576b, {12,6,4}*576b, {8,6,6}*576c, {24,6,2}*576c, {4,6,12}*576c, {12,6,4}*576c, {4,12,6}*576c, {8,6,2}*576, {4,4,4}*576b, {4,6,4}*576a, {4,6,4}*576b, {4,4,6}*576, {4,4,2}*576, {4,12,2}*576, {12,4,2}*576
19-fold covers : {76,2,2}*608, {4,2,38}*608, {4,38,2}*608
20-fold covers : {4,20,4}*640, {4,4,20}*640, {20,4,4}*640, {4,40,2}*640a, {40,4,2}*640a, {4,20,2}*640, {20,4,2}*640, {4,40,2}*640b, {40,4,2}*640b, {8,20,2}*640a, {20,8,2}*640a, {8,20,2}*640b, {20,8,2}*640b, {4,2,40}*640, {40,2,4}*640, {8,2,20}*640, {20,2,8}*640, {4,8,10}*640a, {8,4,10}*640a, {4,10,8}*640, {8,10,4}*640, {4,8,10}*640b, {8,4,10}*640b, {4,4,10}*640, {80,2,2}*640, {16,2,10}*640, {16,10,2}*640
21-fold covers : {12,2,14}*672, {12,14,2}*672, {28,2,6}*672, {28,6,2}*672a, {4,6,14}*672a, {4,14,6}*672, {84,2,2}*672, {4,2,42}*672, {4,42,2}*672a
22-fold covers : {4,44,2}*704, {44,4,2}*704, {4,2,44}*704, {44,2,4}*704, {4,4,22}*704, {4,22,4}*704, {88,2,2}*704, {8,2,22}*704, {8,22,2}*704
23-fold covers : {92,2,2}*736, {4,2,46}*736, {4,46,2}*736
24-fold covers : {4,8,6}*768a, {8,4,6}*768a, {8,12,2}*768a, {12,8,2}*768a, {4,24,2}*768a, {24,4,2}*768a, {8,8,6}*768a, {8,8,6}*768b, {8,8,6}*768c, {8,24,2}*768a, {24,8,2}*768a, {8,24,2}*768b, {8,24,2}*768c, {24,8,2}*768b, {24,8,2}*768c, {8,8,6}*768d, {8,24,2}*768d, {24,8,2}*768d, {8,6,8}*768, {8,2,24}*768, {24,2,8}*768, {8,4,12}*768a, {12,4,8}*768a, {4,12,8}*768a, {8,12,4}*768a, {4,4,24}*768a, {24,4,4}*768a, {8,4,12}*768b, {12,4,8}*768b, {4,12,8}*768b, {8,12,4}*768b, {4,4,24}*768b, {24,4,4}*768b, {4,8,12}*768a, {12,8,4}*768a, {4,24,4}*768a, {4,4,12}*768a, {12,4,4}*768a, {4,12,4}*768a, {4,12,4}*768b, {4,4,12}*768b, {12,4,4}*768b, {4,8,12}*768b, {12,8,4}*768b, {4,24,4}*768b, {4,24,4}*768c, {4,8,12}*768c, {12,8,4}*768c, {4,8,12}*768d, {12,8,4}*768d, {4,24,4}*768d, {4,16,6}*768a, {16,4,6}*768a, {12,16,2}*768a, {16,12,2}*768a, {4,48,2}*768a, {48,4,2}*768a, {4,16,6}*768b, {16,4,6}*768b, {12,16,2}*768b, {16,12,2}*768b, {4,48,2}*768b, {48,4,2}*768b, {4,4,6}*768a, {4,8,6}*768b, {8,4,6}*768b, {4,12,2}*768a, {4,24,2}*768b, {12,4,2}*768a, {24,4,2}*768b, {8,12,2}*768b, {12,8,2}*768b, {4,6,16}*768a, {16,6,4}*768a, {12,2,16}*768, {16,2,12}*768, {4,2,48}*768, {48,2,4}*768, {32,2,6}*768, {32,6,2}*768, {96,2,2}*768, {4,12,4}*768e, {4,12,2}*768d, {12,4,2}*768d, {12,12,2}*768a, {4,4,6}*768e, {4,12,6}*768a, {4,4,12}*768e, {12,4,4}*768e, {4,6,4}*768c, {4,6,4}*768d, {4,12,4}*768g, {4,4,12}*768f, {4,6,12}*768a, {12,6,4}*768a, {12,8,2}*768e, {12,8,2}*768f, {24,4,2}*768c, {24,4,2}*768d, {4,8,6}*768c, {4,12,6}*768b, {8,6,2}*768f, {12,6,2}*768, {12,12,2}*768d, {8,4,6}*768c, {8,6,4}*768a, {8,6,6}*768, {8,6,2}*768g, {24,6,2}*768a, {4,6,6}*768e, {4,8,6}*768d, {4,6,8}*768b, {4,6,8}*768c, {4,6,12}*768b, {4,6,2}*768b, {24,6,2}*768b, {4,12,2}*768e
25-fold covers : {100,2,2}*800, {4,2,50}*800, {4,50,2}*800, {20,2,10}*800, {20,10,2}*800a, {20,10,2}*800b, {4,10,10}*800a, {4,10,10}*800b, {4,10,10}*800c, {20,10,2}*800c, {4,10,2}*800
26-fold covers : {4,52,2}*832, {52,4,2}*832, {4,2,52}*832, {52,2,4}*832, {4,4,26}*832, {4,26,4}*832, {104,2,2}*832, {8,2,26}*832, {8,26,2}*832
27-fold covers : {108,2,2}*864, {4,2,54}*864, {4,54,2}*864a, {36,2,6}*864, {36,6,2}*864a, {36,6,2}*864b, {12,2,18}*864, {12,18,2}*864a, {12,6,6}*864a, {12,6,2}*864a, {12,6,2}*864b, {4,6,18}*864a, {4,18,6}*864a, {4,18,6}*864b, {4,6,6}*864a, {4,6,6}*864b, {4,6,18}*864b, {12,18,2}*864b, {4,6,6}*864c, {12,6,2}*864c, {4,6,2}*864a, {12,6,2}*864e, {12,6,2}*864f, {12,6,6}*864b, {12,6,6}*864c, {12,6,6}*864d, {12,6,6}*864e, {12,6,2}*864g, {4,6,6}*864h, {12,6,6}*864f, {12,6,6}*864g, {4,6,6}*864j, {4,6,6}*864k, {4,6,2}*864b, {12,6,2}*864h, {12,6,2}*864i
28-fold covers : {4,28,4}*896, {4,4,28}*896, {28,4,4}*896, {4,56,2}*896a, {56,4,2}*896a, {4,28,2}*896, {28,4,2}*896, {4,56,2}*896b, {56,4,2}*896b, {8,28,2}*896a, {28,8,2}*896a, {8,28,2}*896b, {28,8,2}*896b, {4,2,56}*896, {56,2,4}*896, {8,2,28}*896, {28,2,8}*896, {4,8,14}*896a, {8,4,14}*896a, {4,14,8}*896, {8,14,4}*896, {4,8,14}*896b, {8,4,14}*896b, {4,4,14}*896, {112,2,2}*896, {16,2,14}*896, {16,14,2}*896
29-fold covers : {116,2,2}*928, {4,2,58}*928, {4,58,2}*928
30-fold covers : {12,2,20}*960, {20,2,12}*960, {4,12,10}*960a, {12,4,10}*960, {4,20,6}*960, {20,4,6}*960, {4,6,20}*960a, {20,6,4}*960a, {4,10,12}*960, {12,10,4}*960, {24,2,10}*960, {24,10,2}*960, {40,2,6}*960, {40,6,2}*960, {8,6,10}*960, {8,10,6}*960, {12,20,2}*960, {20,12,2}*960, {4,60,2}*960a, {60,4,2}*960a, {4,2,60}*960, {60,2,4}*960, {4,4,30}*960, {4,30,4}*960a, {120,2,2}*960, {8,2,30}*960, {8,30,2}*960
31-fold covers : {124,2,2}*992, {4,2,62}*992, {4,62,2}*992
33-fold covers : {12,2,22}*1056, {12,22,2}*1056, {44,2,6}*1056, {44,6,2}*1056a, {4,6,22}*1056a, {4,22,6}*1056, {132,2,2}*1056, {4,2,66}*1056, {4,66,2}*1056a
34-fold covers : {4,4,34}*1088, {4,68,2}*1088, {68,4,2}*1088, {4,34,4}*1088, {4,2,68}*1088, {68,2,4}*1088, {8,2,34}*1088, {8,34,2}*1088, {136,2,2}*1088
35-fold covers : {20,2,14}*1120, {20,14,2}*1120, {28,2,10}*1120, {28,10,2}*1120, {4,10,14}*1120, {4,14,10}*1120, {140,2,2}*1120, {4,2,70}*1120, {4,70,2}*1120
36-fold covers : {4,4,36}*1152, {36,4,4}*1152, {4,36,4}*1152a, {4,12,12}*1152a, {4,12,12}*1152b, {12,12,4}*1152a, {12,12,4}*1152b, {4,12,12}*1152c, {12,12,4}*1152c, {12,4,12}*1152, {4,4,4}*1152a, {4,4,4}*1152b, {4,12,4}*1152a, {4,12,4}*1152b, {4,4,12}*1152, {12,4,4}*1152, {4,8,18}*1152a, {8,4,18}*1152a, {8,36,2}*1152a, {36,8,2}*1152a, {4,72,2}*1152a, {72,4,2}*1152a, {8,12,6}*1152a, {8,12,6}*1152b, {12,8,6}*1152a, {4,24,6}*1152a, {8,12,6}*1152c, {4,24,6}*1152b, {4,24,6}*1152c, {24,4,6}*1152a, {12,24,2}*1152a, {12,24,2}*1152b, {24,12,2}*1152a, {24,12,2}*1152b, {12,24,2}*1152c, {24,12,2}*1152c, {8,4,6}*1152a, {4,8,2}*1152a, {4,24,2}*1152a, {8,4,2}*1152a, {24,4,2}*1152a, {8,12,2}*1152a, {12,8,2}*1152a, {4,8,6}*1152a, {4,8,18}*1152b, {8,4,18}*1152b, {8,36,2}*1152b, {36,8,2}*1152b, {4,72,2}*1152b, {72,4,2}*1152b, {8,12,6}*1152d, {8,12,6}*1152e, {12,8,6}*1152b, {4,24,6}*1152d, {8,12,6}*1152f, {4,24,6}*1152e, {4,24,6}*1152f, {24,4,6}*1152b, {12,24,2}*1152d, {12,24,2}*1152e, {24,12,2}*1152d, {24,12,2}*1152e, {12,24,2}*1152f, {24,12,2}*1152f, {4,8,2}*1152b, {4,24,2}*1152b, {8,4,2}*1152b, {24,4,2}*1152b, {8,4,6}*1152b, {8,12,2}*1152b, {12,8,2}*1152b, {4,8,6}*1152b, {4,4,18}*1152a, {4,36,2}*1152a, {36,4,2}*1152a, {4,12,6}*1152a, {4,12,6}*1152b, {12,4,6}*1152a, {4,12,6}*1152c, {12,12,2}*1152a, {12,12,2}*1152b, {12,12,2}*1152c, {4,4,2}*1152, {4,12,2}*1152, {12,4,2}*1152, {4,4,6}*1152a, {4,18,8}*1152a, {8,18,4}*1152a, {8,2,36}*1152, {36,2,8}*1152, {4,2,72}*1152, {72,2,4}*1152, {8,6,12}*1152a, {12,6,8}*1152a, {8,6,12}*1152b, {12,6,8}*1152b, {8,6,12}*1152c, {12,6,8}*1152c, {4,6,24}*1152a, {24,6,4}*1152a, {4,6,24}*1152b, {24,6,4}*1152b, {4,6,24}*1152c, {24,6,4}*1152c, {12,2,24}*1152, {24,2,12}*1152, {4,6,8}*1152a, {8,4,4}*1152, {8,6,4}*1152a, {4,6,8}*1152b, {8,6,4}*1152b, {16,2,18}*1152, {16,18,2}*1152, {144,2,2}*1152, {16,6,6}*1152a, {16,6,6}*1152b, {16,6,6}*1152c, {48,6,2}*1152a, {48,2,6}*1152, {48,6,2}*1152b, {48,6,2}*1152c, {16,6,2}*1152, {36,4,2}*1152b, {4,4,18}*1152d, {4,18,4}*1152a, {4,18,2}*1152b, {12,4,6}*1152b, {12,12,2}*1152d, {12,12,2}*1152e, {12,4,6}*1152c, {12,6,4}*1152a, {12,6,6}*1152a, {12,6,2}*1152a, {12,6,2}*1152b, {4,6,6}*1152c, {4,6,6}*1152d, {4,6,6}*1152e, {4,6,12}*1152b, {4,6,12}*1152c, {4,12,6}*1152g, {12,6,6}*1152b, {4,6,6}*1152f, {4,12,6}*1152j, {12,6,4}*1152d, {12,6,2}*1152e, {12,6,2}*1152f
37-fold covers : {4,2,74}*1184, {4,74,2}*1184, {148,2,2}*1184
38-fold covers : {4,4,38}*1216, {4,76,2}*1216, {76,4,2}*1216, {4,38,4}*1216, {4,2,76}*1216, {76,2,4}*1216, {8,2,38}*1216, {8,38,2}*1216, {152,2,2}*1216
39-fold covers : {12,2,26}*1248, {12,26,2}*1248, {52,2,6}*1248, {52,6,2}*1248a, {4,6,26}*1248a, {4,26,6}*1248, {156,2,2}*1248, {4,2,78}*1248, {4,78,2}*1248a
40-fold covers : {4,8,10}*1280a, {8,4,10}*1280a, {8,20,2}*1280a, {20,8,2}*1280a, {4,40,2}*1280a, {40,4,2}*1280a, {8,8,10}*1280a, {8,8,10}*1280b, {8,8,10}*1280c, {8,40,2}*1280a, {40,8,2}*1280a, {8,40,2}*1280b, {8,40,2}*1280c, {40,8,2}*1280b, {40,8,2}*1280c, {8,8,10}*1280d, {8,40,2}*1280d, {40,8,2}*1280d, {8,10,8}*1280, {8,2,40}*1280, {40,2,8}*1280, {8,4,20}*1280a, {20,4,8}*1280a, {4,20,8}*1280a, {8,20,4}*1280a, {4,4,40}*1280a, {40,4,4}*1280a, {8,4,20}*1280b, {20,4,8}*1280b, {4,20,8}*1280b, {8,20,4}*1280b, {4,4,40}*1280b, {40,4,4}*1280b, {4,8,20}*1280a, {20,8,4}*1280a, {4,40,4}*1280a, {4,4,20}*1280a, {20,4,4}*1280a, {4,20,4}*1280a, {4,20,4}*1280b, {4,4,20}*1280b, {20,4,4}*1280b, {4,8,20}*1280b, {20,8,4}*1280b, {4,40,4}*1280b, {4,40,4}*1280c, {4,8,20}*1280c, {20,8,4}*1280c, {4,8,20}*1280d, {20,8,4}*1280d, {4,40,4}*1280d, {4,16,10}*1280a, {16,4,10}*1280a, {16,20,2}*1280a, {20,16,2}*1280a, {4,80,2}*1280a, {80,4,2}*1280a, {4,16,10}*1280b, {16,4,10}*1280b, {16,20,2}*1280b, {20,16,2}*1280b, {4,80,2}*1280b, {80,4,2}*1280b, {4,4,10}*1280, {4,8,10}*1280b, {8,4,10}*1280b, {4,20,2}*1280a, {4,40,2}*1280b, {20,4,2}*1280a, {40,4,2}*1280b, {8,20,2}*1280b, {20,8,2}*1280b, {4,10,16}*1280, {16,10,4}*1280, {16,2,20}*1280, {20,2,16}*1280, {4,2,80}*1280, {80,2,4}*1280, {32,2,10}*1280, {32,10,2}*1280, {160,2,2}*1280
41-fold covers : {4,2,82}*1312, {4,82,2}*1312, {164,2,2}*1312
42-fold covers : {12,2,28}*1344, {28,2,12}*1344, {4,6,28}*1344a, {28,6,4}*1344a, {4,14,12}*1344, {12,14,4}*1344, {4,12,14}*1344a, {12,4,14}*1344, {4,28,6}*1344, {28,4,6}*1344, {24,2,14}*1344, {24,14,2}*1344, {56,2,6}*1344, {56,6,2}*1344, {8,6,14}*1344, {8,14,6}*1344, {12,28,2}*1344, {28,12,2}*1344, {4,84,2}*1344a, {84,4,2}*1344a, {4,2,84}*1344, {84,2,4}*1344, {4,4,42}*1344, {4,42,4}*1344a, {168,2,2}*1344, {8,2,42}*1344, {8,42,2}*1344
43-fold covers : {4,2,86}*1376, {4,86,2}*1376, {172,2,2}*1376
44-fold covers : {4,4,44}*1408, {44,4,4}*1408, {4,44,4}*1408, {4,8,22}*1408a, {8,4,22}*1408a, {8,44,2}*1408a, {44,8,2}*1408a, {4,88,2}*1408a, {88,4,2}*1408a, {4,8,22}*1408b, {8,4,22}*1408b, {8,44,2}*1408b, {44,8,2}*1408b, {4,88,2}*1408b, {88,4,2}*1408b, {4,4,22}*1408, {4,44,2}*1408, {44,4,2}*1408, {4,22,8}*1408, {8,22,4}*1408, {8,2,44}*1408, {44,2,8}*1408, {4,2,88}*1408, {88,2,4}*1408, {16,2,22}*1408, {16,22,2}*1408, {176,2,2}*1408
45-fold covers : {36,2,10}*1440, {36,10,2}*1440, {20,2,18}*1440, {20,18,2}*1440a, {4,10,18}*1440, {4,18,10}*1440a, {180,2,2}*1440, {4,2,90}*1440, {4,90,2}*1440a, {12,6,10}*1440a, {12,6,10}*1440b, {12,10,6}*1440, {20,6,6}*1440a, {20,6,6}*1440b, {20,6,6}*1440c, {60,6,2}*1440a, {12,30,2}*1440a, {4,30,6}*1440a, {12,6,10}*1440c, {4,6,30}*1440a, {12,2,30}*1440, {12,30,2}*1440b, {60,2,6}*1440, {60,6,2}*1440b, {60,6,2}*1440c, {4,6,30}*1440b, {4,30,6}*1440b, {4,30,6}*1440c, {4,6,30}*1440c, {12,30,2}*1440c, {4,6,10}*1440, {4,30,2}*1440, {20,6,2}*1440
46-fold covers : {4,4,46}*1472, {4,92,2}*1472, {92,4,2}*1472, {4,46,4}*1472, {4,2,92}*1472, {92,2,4}*1472, {8,2,46}*1472, {8,46,2}*1472, {184,2,2}*1472
47-fold covers : {4,2,94}*1504, {4,94,2}*1504, {188,2,2}*1504
49-fold covers : {196,2,2}*1568, {4,2,98}*1568, {4,98,2}*1568, {28,2,14}*1568, {28,14,2}*1568a, {28,14,2}*1568b, {4,14,14}*1568a, {4,14,14}*1568b, {4,14,14}*1568c, {28,14,2}*1568c, {4,14,2}*1568
50-fold covers : {4,100,2}*1600, {100,4,2}*1600, {4,2,100}*1600, {100,2,4}*1600, {4,4,50}*1600, {4,50,4}*1600, {200,2,2}*1600, {8,2,50}*1600, {8,50,2}*1600, {20,2,20}*1600, {4,10,20}*1600a, {20,10,4}*1600a, {4,20,10}*1600a, {4,20,10}*1600b, {20,4,10}*1600, {40,2,10}*1600, {40,10,2}*1600a, {40,10,2}*1600b, {8,10,10}*1600a, {8,10,10}*1600b, {20,20,2}*1600a, {20,20,2}*1600b, {20,20,2}*1600c, {4,10,20}*1600b, {20,10,4}*1600b, {4,10,20}*1600c, {20,10,4}*1600c, {8,10,10}*1600c, {40,10,2}*1600c, {4,20,10}*1600c, {8,10,2}*1600, {4,4,4}*1600a, {4,10,4}*1600a, {4,10,4}*1600b, {4,4,10}*1600, {4,4,2}*1600, {4,20,2}*1600, {20,4,2}*1600
51-fold covers : {12,2,34}*1632, {12,34,2}*1632, {68,2,6}*1632, {68,6,2}*1632a, {4,6,34}*1632a, {4,34,6}*1632, {204,2,2}*1632, {4,2,102}*1632, {4,102,2}*1632a
52-fold covers : {4,4,52}*1664, {52,4,4}*1664, {4,52,4}*1664, {4,8,26}*1664a, {8,4,26}*1664a, {8,52,2}*1664a, {52,8,2}*1664a, {4,104,2}*1664a, {104,4,2}*1664a, {4,8,26}*1664b, {8,4,26}*1664b, {8,52,2}*1664b, {52,8,2}*1664b, {4,104,2}*1664b, {104,4,2}*1664b, {4,4,26}*1664, {4,52,2}*1664, {52,4,2}*1664, {4,26,8}*1664, {8,26,4}*1664, {8,2,52}*1664, {52,2,8}*1664, {4,2,104}*1664, {104,2,4}*1664, {16,2,26}*1664, {16,26,2}*1664, {208,2,2}*1664
53-fold covers : {4,2,106}*1696, {4,106,2}*1696, {212,2,2}*1696
54-fold covers : {4,108,2}*1728a, {108,4,2}*1728a, {4,2,108}*1728, {108,2,4}*1728, {4,4,54}*1728, {4,54,4}*1728a, {216,2,2}*1728, {8,2,54}*1728, {8,54,2}*1728, {12,2,36}*1728, {36,2,12}*1728, {12,6,12}*1728a, {4,6,36}*1728a, {36,6,4}*1728a, {4,18,12}*1728a, {12,18,4}*1728a, {4,12,18}*1728a, {12,4,18}*1728, {4,36,6}*1728a, {4,36,6}*1728b, {36,4,6}*1728, {4,6,12}*1728a, {12,6,4}*1728a, {4,12,6}*1728a, {4,12,6}*1728b, {12,12,6}*1728a, {72,2,6}*1728, {72,6,2}*1728a, {72,6,2}*1728b, {24,2,18}*1728, {24,18,2}*1728a, {24,6,6}*1728a, {24,6,2}*1728a, {24,6,2}*1728b, {8,6,18}*1728a, {8,18,6}*1728a, {8,18,6}*1728b, {8,6,6}*1728a, {8,6,6}*1728b, {12,36,2}*1728a, {12,36,2}*1728b, {36,12,2}*1728a, {36,12,2}*1728b, {4,6,36}*1728b, {36,6,4}*1728b, {12,12,2}*1728a, {12,12,2}*1728b, {12,12,2}*1728c, {4,6,12}*1728b, {12,6,4}*1728b, {8,6,18}*1728b, {24,18,2}*1728b, {4,18,12}*1728b, {12,18,4}*1728b, {8,6,6}*1728c, {24,6,2}*1728c, {4,6,12}*1728c, {12,6,4}*1728c, {4,12,18}*1728b, {4,12,6}*1728c, {8,6,2}*1728a, {24,6,2}*1728d, {24,6,2}*1728e, {4,4,12}*1728a, {4,6,4}*1728a, {4,6,4}*1728b, {4,6,12}*1728f, {4,6,12}*1728g, {4,12,4}*1728a, {12,6,4}*1728f, {12,6,4}*1728g, {4,4,6}*1728a, {4,12,6}*1728h, {4,12,6}*1728i, {4,12,2}*1728a, {4,12,2}*1728b, {12,4,2}*1728a, {12,4,2}*1728b, {12,12,2}*1728d, {12,12,2}*1728e, {12,12,2}*1728f, {12,12,2}*1728g, {24,6,6}*1728b, {24,6,6}*1728c, {24,6,6}*1728d, {24,6,6}*1728e, {24,6,2}*1728f, {12,6,12}*1728b, {12,6,12}*1728c, {12,6,12}*1728d, {12,6,12}*1728e, {12,6,12}*1728f, {12,12,6}*1728b, {12,12,6}*1728c, {12,12,6}*1728d, {12,12,6}*1728e, {12,12,6}*1728f, {8,6,6}*1728e, {24,6,6}*1728f, {24,6,6}*1728g, {12,12,2}*1728h, {12,6,12}*1728g, {4,12,6}*1728j, {12,12,6}*1728g, {4,6,12}*1728h, {12,6,4}*1728h, {8,6,6}*1728f, {4,6,12}*1728k, {4,6,12}*1728l, {12,4,4}*1728b, {12,6,4}*1728k, {12,6,4}*1728l, {12,4,6}*1728a, {4,12,2}*1728c, {4,12,2}*1728d, {12,4,2}*1728c, {12,4,2}*1728d, {12,12,2}*1728i, {12,12,2}*1728j, {8,6,6}*1728g, {8,6,2}*1728b, {24,6,2}*1728g, {4,4,6}*1728b, {4,4,6}*1728c, {4,12,6}*1728n, {4,12,6}*1728o, {4,12,6}*1728p, {12,4,6}*1728b, {4,6,4}*1728c, {4,6,4}*1728d, {4,12,4}*1728d, {4,4,12}*1728c, {4,6,12}*1728m, {12,6,4}*1728m, {24,6,2}*1728h, {4,6,12}*1728n, {12,6,4}*1728n, {4,12,6}*1728q, {12,12,2}*1728k, {12,12,2}*1728l
55-fold covers : {20,2,22}*1760, {20,22,2}*1760, {44,2,10}*1760, {44,10,2}*1760, {4,10,22}*1760, {4,22,10}*1760, {220,2,2}*1760, {4,2,110}*1760, {4,110,2}*1760
56-fold covers : {4,8,14}*1792a, {8,4,14}*1792a, {8,28,2}*1792a, {28,8,2}*1792a, {4,56,2}*1792a, {56,4,2}*1792a, {8,8,14}*1792a, {8,8,14}*1792b, {8,8,14}*1792c, {8,56,2}*1792a, {56,8,2}*1792a, {8,56,2}*1792b, {8,56,2}*1792c, {56,8,2}*1792b, {56,8,2}*1792c, {8,8,14}*1792d, {8,56,2}*1792d, {56,8,2}*1792d, {8,14,8}*1792, {8,2,56}*1792, {56,2,8}*1792, {8,4,28}*1792a, {28,4,8}*1792a, {4,28,8}*1792a, {8,28,4}*1792a, {4,4,56}*1792a, {56,4,4}*1792a, {8,4,28}*1792b, {28,4,8}*1792b, {4,28,8}*1792b, {8,28,4}*1792b, {4,4,56}*1792b, {56,4,4}*1792b, {4,8,28}*1792a, {28,8,4}*1792a, {4,56,4}*1792a, {4,4,28}*1792a, {28,4,4}*1792a, {4,28,4}*1792a, {4,28,4}*1792b, {4,4,28}*1792b, {28,4,4}*1792b, {4,8,28}*1792b, {28,8,4}*1792b, {4,56,4}*1792b, {4,56,4}*1792c, {4,8,28}*1792c, {28,8,4}*1792c, {4,8,28}*1792d, {28,8,4}*1792d, {4,56,4}*1792d, {4,16,14}*1792a, {16,4,14}*1792a, {16,28,2}*1792a, {28,16,2}*1792a, {4,112,2}*1792a, {112,4,2}*1792a, {4,16,14}*1792b, {16,4,14}*1792b, {16,28,2}*1792b, {28,16,2}*1792b, {4,112,2}*1792b, {112,4,2}*1792b, {4,4,14}*1792, {4,8,14}*1792b, {8,4,14}*1792b, {4,28,2}*1792, {4,56,2}*1792b, {28,4,2}*1792, {56,4,2}*1792b, {8,28,2}*1792b, {28,8,2}*1792b, {4,14,16}*1792, {16,14,4}*1792, {16,2,28}*1792, {28,2,16}*1792, {4,2,112}*1792, {112,2,4}*1792, {32,2,14}*1792, {32,14,2}*1792, {224,2,2}*1792
57-fold covers : {12,2,38}*1824, {12,38,2}*1824, {76,2,6}*1824, {76,6,2}*1824a, {4,6,38}*1824a, {4,38,6}*1824, {228,2,2}*1824, {4,2,114}*1824, {4,114,2}*1824a
58-fold covers : {4,4,58}*1856, {4,116,2}*1856, {116,4,2}*1856, {4,58,4}*1856, {4,2,116}*1856, {116,2,4}*1856, {8,2,58}*1856, {8,58,2}*1856, {232,2,2}*1856
59-fold covers : {4,2,118}*1888, {4,118,2}*1888, {236,2,2}*1888
60-fold covers : {4,4,60}*1920, {60,4,4}*1920, {4,60,4}*1920a, {4,20,12}*1920, {12,20,4}*1920, {4,12,20}*1920a, {20,12,4}*1920a, {12,4,20}*1920, {20,4,12}*1920, {4,8,30}*1920a, {8,4,30}*1920a, {8,60,2}*1920a, {60,8,2}*1920a, {4,120,2}*1920a, {120,4,2}*1920a, {8,12,10}*1920a, {12,8,10}*1920a, {8,20,6}*1920a, {20,8,6}*1920a, {4,24,10}*1920a, {24,4,10}*1920a, {4,40,6}*1920a, {40,4,6}*1920a, {12,40,2}*1920a, {40,12,2}*1920a, {20,24,2}*1920a, {24,20,2}*1920a, {4,8,30}*1920b, {8,4,30}*1920b, {8,60,2}*1920b, {60,8,2}*1920b, {4,120,2}*1920b, {120,4,2}*1920b, {8,12,10}*1920b, {12,8,10}*1920b, {8,20,6}*1920b, {20,8,6}*1920b, {4,24,10}*1920b, {24,4,10}*1920b, {4,40,6}*1920b, {40,4,6}*1920b, {12,40,2}*1920b, {40,12,2}*1920b, {20,24,2}*1920b, {24,20,2}*1920b, {4,4,30}*1920a, {4,60,2}*1920a, {60,4,2}*1920a, {4,12,10}*1920a, {12,4,10}*1920a, {4,20,6}*1920a, {20,4,6}*1920a, {12,20,2}*1920a, {20,12,2}*1920a, {4,30,8}*1920a, {8,30,4}*1920a, {8,2,60}*1920, {60,2,8}*1920, {4,2,120}*1920, {120,2,4}*1920, {8,10,12}*1920, {12,10,8}*1920, {8,6,20}*1920, {20,6,8}*1920, {4,10,24}*1920, {24,10,4}*1920, {4,6,40}*1920a, {40,6,4}*1920a, {12,2,40}*1920, {40,2,12}*1920, {20,2,24}*1920, {24,2,20}*1920, {16,2,30}*1920, {16,30,2}*1920, {240,2,2}*1920, {16,6,10}*1920, {16,10,6}*1920, {48,2,10}*1920, {48,10,2}*1920, {80,2,6}*1920, {80,6,2}*1920, {12,4,10}*1920b, {12,20,2}*1920b, {20,4,6}*1920b, {20,6,4}*1920a, {20,6,6}*1920, {20,6,2}*1920a, {60,6,2}*1920a, {4,6,10}*1920b, {4,6,20}*1920b, {4,20,6}*1920c, {4,30,6}*1920, {12,6,10}*1920a, {4,6,30}*1920, {12,30,2}*1920b, {60,4,2}*1920b, {4,4,30}*1920d, {4,30,4}*1920a, {4,30,2}*1920b, {4,4,10}*1920c, {4,6,10}*1920c, {4,10,2}*1920, {12,6,2}*1920a, {12,10,2}*1920b, {4,4,6}*1920a, {4,6,4}*1920a, {4,6,6}*1920a, {4,10,4}*1920a, {4,10,6}*1920b, {12,6,6}*1920, {4,6,2}*1920, {12,4,2}*1920b, {20,4,2}*1920a, {20,6,2}*1920b, {4,6,10}*1920d, {4,10,6}*1920c, {4,10,10}*1920, {12,10,2}*1920c, {20,6,2}*1920c, {20,10,2}*1920a
61-fold covers : {4,2,122}*1952, {4,122,2}*1952, {244,2,2}*1952
62-fold covers : {4,4,62}*1984, {4,124,2}*1984, {124,4,2}*1984, {4,62,4}*1984, {4,2,124}*1984, {124,2,4}*1984, {8,2,62}*1984, {8,62,2}*1984, {248,2,2}*1984
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := (5,6);;
s3 := (7,8);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(8)!(2,3);
s1 := Sym(8)!(1,2)(3,4);
s2 := Sym(8)!(5,6);
s3 := Sym(8)!(7,8);
poly := sub<Sym(8)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope