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# Polytope of Type {2,2,4}

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

```
Permutation Representation (Magma) :
```s0 := Sym(8)!(1,2);
s1 := Sym(8)!(3,4);
s2 := Sym(8)!(6,7);
s3 := Sym(8)!(5,6)(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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope