Polytope of Type {6,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,2}*48
if this polytope has a name.
Group : SmallGroup(48,51)
Rank : 4
Schlafli Type : {6,2,2}
Number of vertices, edges, etc : 6, 6, 2, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,2,2,2} of size 96
{6,2,2,3} of size 144
{6,2,2,4} of size 192
{6,2,2,5} of size 240
{6,2,2,6} of size 288
{6,2,2,7} of size 336
{6,2,2,8} of size 384
{6,2,2,9} of size 432
{6,2,2,10} of size 480
{6,2,2,11} of size 528
{6,2,2,12} of size 576
{6,2,2,13} of size 624
{6,2,2,14} of size 672
{6,2,2,15} of size 720
{6,2,2,16} of size 768
{6,2,2,17} of size 816
{6,2,2,18} of size 864
{6,2,2,19} of size 912
{6,2,2,20} of size 960
{6,2,2,21} of size 1008
{6,2,2,22} of size 1056
{6,2,2,23} of size 1104
{6,2,2,24} of size 1152
{6,2,2,25} of size 1200
{6,2,2,26} of size 1248
{6,2,2,27} of size 1296
{6,2,2,28} of size 1344
{6,2,2,29} of size 1392
{6,2,2,30} of size 1440
{6,2,2,31} of size 1488
{6,2,2,33} of size 1584
{6,2,2,34} of size 1632
{6,2,2,35} of size 1680
{6,2,2,36} of size 1728
{6,2,2,37} of size 1776
{6,2,2,38} of size 1824
{6,2,2,39} of size 1872
{6,2,2,40} of size 1920
{6,2,2,41} of size 1968
Vertex Figure Of :
{2,6,2,2} of size 96
{3,6,2,2} of size 144
{4,6,2,2} of size 192
{3,6,2,2} of size 192
{4,6,2,2} of size 192
{4,6,2,2} of size 192
{4,6,2,2} of size 288
{6,6,2,2} of size 288
{6,6,2,2} of size 288
{6,6,2,2} of size 288
{8,6,2,2} of size 384
{4,6,2,2} of size 384
{6,6,2,2} of size 384
{9,6,2,2} of size 432
{3,6,2,2} of size 432
{6,6,2,2} of size 432
{4,6,2,2} of size 480
{5,6,2,2} of size 480
{6,6,2,2} of size 480
{5,6,2,2} of size 480
{5,6,2,2} of size 480
{10,6,2,2} of size 480
{12,6,2,2} of size 576
{12,6,2,2} of size 576
{12,6,2,2} of size 576
{3,6,2,2} of size 576
{12,6,2,2} of size 576
{4,6,2,2} of size 576
{14,6,2,2} of size 672
{15,6,2,2} of size 720
{16,6,2,2} of size 768
{3,6,2,2} of size 768
{8,6,2,2} of size 768
{4,6,2,2} of size 768
{6,6,2,2} of size 768
{4,6,2,2} of size 768
{12,6,2,2} of size 768
{8,6,2,2} of size 768
{12,6,2,2} of size 768
{6,6,2,2} of size 768
{8,6,2,2} of size 768
{4,6,2,2} of size 864
{12,6,2,2} of size 864
{12,6,2,2} of size 864
{18,6,2,2} of size 864
{18,6,2,2} of size 864
{6,6,2,2} of size 864
{6,6,2,2} of size 864
{6,6,2,2} of size 864
{12,6,2,2} of size 864
{6,6,2,2} of size 864
{20,6,2,2} of size 960
{4,6,2,2} of size 960
{4,6,2,2} of size 960
{4,6,2,2} of size 960
{5,6,2,2} of size 960
{6,6,2,2} of size 960
{6,6,2,2} of size 960
{6,6,2,2} of size 960
{10,6,2,2} of size 960
{10,6,2,2} of size 960
{5,6,2,2} of size 960
{10,6,2,2} of size 960
{10,6,2,2} of size 960
{10,6,2,2} of size 960
{10,6,2,2} of size 960
{15,6,2,2} of size 960
{20,6,2,2} of size 960
{21,6,2,2} of size 1008
{22,6,2,2} of size 1056
{24,6,2,2} of size 1152
{24,6,2,2} of size 1152
{24,6,2,2} of size 1152
{8,6,2,2} of size 1152
{6,6,2,2} of size 1152
{6,6,2,2} of size 1152
{12,6,2,2} of size 1152
{12,6,2,2} of size 1152
{3,6,2,2} of size 1200
{10,6,2,2} of size 1200
{26,6,2,2} of size 1248
{9,6,2,2} of size 1296
{18,6,2,2} of size 1296
{27,6,2,2} of size 1296
{6,6,2,2} of size 1296
{6,6,2,2} of size 1296
{9,6,2,2} of size 1296
{9,6,2,2} of size 1296
{9,6,2,2} of size 1296
{18,6,2,2} of size 1296
{3,6,2,2} of size 1296
{18,6,2,2} of size 1296
{28,6,2,2} of size 1344
{4,6,2,2} of size 1344
{6,6,2,2} of size 1344
{7,6,2,2} of size 1344
{8,6,2,2} of size 1344
{8,6,2,2} of size 1344
{21,6,2,2} of size 1344
{28,6,2,2} of size 1344
{15,6,2,2} of size 1440
{20,6,2,2} of size 1440
{30,6,2,2} of size 1440
{30,6,2,2} of size 1440
{30,6,2,2} of size 1440
{33,6,2,2} of size 1584
{34,6,2,2} of size 1632
{36,6,2,2} of size 1728
{36,6,2,2} of size 1728
{12,6,2,2} of size 1728
{12,6,2,2} of size 1728
{12,6,2,2} of size 1728
{9,6,2,2} of size 1728
{36,6,2,2} of size 1728
{3,6,2,2} of size 1728
{12,6,2,2} of size 1728
{4,6,2,2} of size 1728
{12,6,2,2} of size 1728
{12,6,2,2} of size 1728
{12,6,2,2} of size 1728
{4,6,2,2} of size 1728
{12,6,2,2} of size 1728
{12,6,2,2} of size 1728
{38,6,2,2} of size 1824
{39,6,2,2} of size 1872
{40,6,2,2} of size 1920
{20,6,2,2} of size 1920
{30,6,2,2} of size 1920
{12,6,2,2} of size 1920
{12,6,2,2} of size 1920
{20,6,2,2} of size 1920
{20,6,2,2} of size 1920
{4,6,2,2} of size 1920
{6,6,2,2} of size 1920
{10,6,2,2} of size 1920
{10,6,2,2} of size 1920
{5,6,2,2} of size 1920
{8,6,2,2} of size 1920
{8,6,2,2} of size 1920
{10,6,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,2}*24
3-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,2,2}*96, {6,2,4}*96, {6,4,2}*96a
3-fold covers : {18,2,2}*144, {6,2,6}*144, {6,6,2}*144a, {6,6,2}*144c
4-fold covers : {12,4,2}*192a, {12,2,4}*192, {6,4,4}*192, {24,2,2}*192, {6,2,8}*192, {6,8,2}*192, {6,4,2}*192
5-fold covers : {6,2,10}*240, {6,10,2}*240, {30,2,2}*240
6-fold covers : {36,2,2}*288, {18,2,4}*288, {18,4,2}*288a, {6,2,12}*288, {6,12,2}*288a, {12,2,6}*288, {12,6,2}*288a, {12,6,2}*288b, {6,4,6}*288, {6,6,4}*288a, {6,6,4}*288c, {6,12,2}*288c
7-fold covers : {6,2,14}*336, {6,14,2}*336, {42,2,2}*336
8-fold covers : {12,4,4}*384, {24,4,2}*384a, {12,4,2}*384a, {24,4,2}*384b, {12,8,2}*384a, {12,8,2}*384b, {24,2,4}*384, {12,2,8}*384, {6,4,8}*384a, {6,8,4}*384a, {6,4,8}*384b, {6,8,4}*384b, {6,4,4}*384a, {48,2,2}*384, {6,2,16}*384, {6,16,2}*384, {12,4,2}*384b, {6,4,4}*384d, {6,4,2}*384b, {12,4,2}*384c, {6,8,2}*384b, {6,8,2}*384c
9-fold covers : {54,2,2}*432, {6,2,18}*432, {6,18,2}*432a, {18,2,6}*432, {18,6,2}*432a, {18,6,2}*432b, {6,6,6}*432a, {6,6,2}*432b, {6,6,2}*432c, {6,6,6}*432b, {6,6,6}*432c, {6,6,6}*432e, {6,6,6}*432g, {6,6,2}*432d
10-fold covers : {12,2,10}*480, {12,10,2}*480, {6,2,20}*480, {6,20,2}*480a, {6,4,10}*480, {6,10,4}*480, {60,2,2}*480, {30,2,4}*480, {30,4,2}*480a
11-fold covers : {6,2,22}*528, {6,22,2}*528, {66,2,2}*528
12-fold covers : {36,4,2}*576a, {36,2,4}*576, {18,4,4}*576, {72,2,2}*576, {18,2,8}*576, {18,8,2}*576, {12,2,12}*576, {6,4,12}*576, {6,12,4}*576a, {12,4,6}*576, {12,6,4}*576a, {6,2,24}*576, {6,24,2}*576a, {24,2,6}*576, {24,6,2}*576a, {24,6,2}*576b, {6,6,8}*576a, {6,8,6}*576, {12,12,2}*576a, {12,12,2}*576c, {12,6,4}*576b, {6,6,8}*576c, {6,24,2}*576c, {6,12,4}*576c, {18,4,2}*576, {6,4,6}*576a, {6,4,6}*576b, {6,6,4}*576a, {6,6,6}*576a, {6,6,2}*576b, {6,12,2}*576a, {6,12,2}*576b, {12,6,2}*576a
13-fold covers : {6,2,26}*624, {6,26,2}*624, {78,2,2}*624
14-fold covers : {12,2,14}*672, {12,14,2}*672, {6,2,28}*672, {6,28,2}*672a, {6,4,14}*672, {6,14,4}*672, {84,2,2}*672, {42,2,4}*672, {42,4,2}*672a
15-fold covers : {18,2,10}*720, {18,10,2}*720, {90,2,2}*720, {6,6,10}*720a, {6,6,10}*720c, {6,10,6}*720, {6,30,2}*720a, {6,2,30}*720, {6,30,2}*720b, {30,2,6}*720, {30,6,2}*720b, {30,6,2}*720c
16-fold covers : {6,4,8}*768a, {6,8,4}*768a, {12,8,2}*768a, {24,4,2}*768a, {6,8,8}*768a, {6,8,8}*768b, {6,8,8}*768c, {24,8,2}*768a, {24,8,2}*768b, {24,8,2}*768c, {6,8,8}*768d, {24,8,2}*768d, {24,2,8}*768, {12,4,8}*768a, {24,4,4}*768a, {12,4,8}*768b, {24,4,4}*768b, {12,8,4}*768a, {12,4,4}*768a, {12,4,4}*768b, {12,8,4}*768b, {12,8,4}*768c, {12,8,4}*768d, {6,4,16}*768a, {6,16,4}*768a, {12,16,2}*768a, {48,4,2}*768a, {6,4,16}*768b, {6,16,4}*768b, {12,16,2}*768b, {48,4,2}*768b, {6,4,4}*768a, {6,4,8}*768b, {6,8,4}*768b, {12,4,2}*768a, {24,4,2}*768b, {12,8,2}*768b, {12,2,16}*768, {48,2,4}*768, {6,2,32}*768, {6,32,2}*768, {96,2,2}*768, {12,4,2}*768d, {6,4,4}*768e, {12,4,4}*768e, {12,4,4}*768f, {6,8,2}*768d, {6,8,2}*768e, {6,4,4}*768f, {6,4,2}*768a, {12,8,2}*768e, {12,8,2}*768f, {24,4,2}*768c, {24,4,2}*768d, {6,8,4}*768c, {6,8,2}*768f, {12,8,2}*768g, {12,8,2}*768h, {6,4,8}*768c, {6,8,2}*768g, {6,8,4}*768d, {6,4,2}*768b, {24,4,2}*768e, {12,4,2}*768e, {24,4,2}*768f
17-fold covers : {6,2,34}*816, {6,34,2}*816, {102,2,2}*816
18-fold covers : {108,2,2}*864, {54,2,4}*864, {54,4,2}*864a, {6,2,36}*864, {6,36,2}*864a, {36,2,6}*864, {36,6,2}*864a, {36,6,2}*864b, {12,2,18}*864, {12,18,2}*864a, {18,2,12}*864, {18,12,2}*864a, {6,6,12}*864a, {12,6,6}*864a, {6,12,2}*864b, {12,6,2}*864a, {12,6,2}*864b, {6,4,18}*864, {6,18,4}*864a, {18,4,6}*864, {18,6,4}*864a, {6,6,4}*864b, {6,12,6}*864a, {18,6,4}*864b, {18,12,2}*864b, {6,6,4}*864c, {6,12,2}*864c, {6,6,12}*864b, {6,6,12}*864c, {6,12,6}*864b, {6,12,6}*864d, {12,6,6}*864b, {12,6,6}*864c, {12,6,6}*864d, {6,6,12}*864e, {12,6,6}*864e, {6,12,2}*864g, {12,6,2}*864g, {6,6,4}*864h, {6,6,12}*864f, {6,12,6}*864f, {6,12,6}*864g, {6,4,4}*864b, {6,4,6}*864a, {6,6,4}*864j, {6,6,4}*864k, {6,4,2}*864b, {12,4,2}*864b, {12,6,2}*864i
19-fold covers : {6,2,38}*912, {6,38,2}*912, {114,2,2}*912
20-fold covers : {12,2,20}*960, {12,4,10}*960, {6,4,20}*960, {6,20,4}*960, {12,10,4}*960, {24,2,10}*960, {24,10,2}*960, {6,2,40}*960, {6,40,2}*960, {6,8,10}*960, {6,10,8}*960, {12,20,2}*960, {60,4,2}*960a, {60,2,4}*960, {30,4,4}*960, {120,2,2}*960, {30,2,8}*960, {30,8,2}*960, {6,4,10}*960, {6,20,2}*960c, {30,4,2}*960
21-fold covers : {18,2,14}*1008, {18,14,2}*1008, {126,2,2}*1008, {6,6,14}*1008a, {6,6,14}*1008c, {6,14,6}*1008, {6,42,2}*1008a, {6,2,42}*1008, {6,42,2}*1008b, {42,2,6}*1008, {42,6,2}*1008b, {42,6,2}*1008c
22-fold covers : {12,2,22}*1056, {12,22,2}*1056, {6,2,44}*1056, {6,44,2}*1056a, {6,4,22}*1056, {6,22,4}*1056, {132,2,2}*1056, {66,2,4}*1056, {66,4,2}*1056a
23-fold covers : {6,2,46}*1104, {6,46,2}*1104, {138,2,2}*1104
24-fold covers : {36,4,4}*1152, {12,12,4}*1152b, {12,12,4}*1152c, {12,4,12}*1152, {18,4,8}*1152a, {18,8,4}*1152a, {36,8,2}*1152a, {72,4,2}*1152a, {6,8,12}*1152a, {6,12,8}*1152b, {12,8,6}*1152a, {6,12,8}*1152c, {6,24,4}*1152a, {6,4,24}*1152a, {6,24,4}*1152c, {24,4,6}*1152a, {12,24,2}*1152a, {24,12,2}*1152a, {24,12,2}*1152b, {12,24,2}*1152c, {18,4,8}*1152b, {18,8,4}*1152b, {36,8,2}*1152b, {72,4,2}*1152b, {6,8,12}*1152b, {6,12,8}*1152e, {12,8,6}*1152b, {6,12,8}*1152f, {6,24,4}*1152d, {6,4,24}*1152b, {6,24,4}*1152f, {24,4,6}*1152b, {12,24,2}*1152d, {24,12,2}*1152d, {24,12,2}*1152e, {12,24,2}*1152f, {18,4,4}*1152a, {36,4,2}*1152a, {6,4,12}*1152a, {6,12,4}*1152b, {12,4,6}*1152a, {6,12,4}*1152c, {12,12,2}*1152a, {12,12,2}*1152c, {36,2,8}*1152, {72,2,4}*1152, {12,6,8}*1152b, {12,6,8}*1152c, {24,6,4}*1152b, {24,6,4}*1152c, {12,2,24}*1152, {24,2,12}*1152, {18,2,16}*1152, {18,16,2}*1152, {144,2,2}*1152, {6,6,16}*1152b, {6,16,6}*1152, {6,6,16}*1152c, {6,48,2}*1152a, {6,2,48}*1152, {6,48,2}*1152b, {48,2,6}*1152, {48,6,2}*1152b, {48,6,2}*1152c, {36,4,2}*1152b, {18,4,4}*1152d, {18,4,2}*1152b, {36,4,2}*1152c, {18,8,2}*1152b, {18,8,2}*1152c, {6,4,12}*1152b, {6,12,4}*1152e, {12,4,6}*1152b, {12,12,2}*1152d, {12,12,2}*1152e, {12,12,2}*1152f, {6,4,12}*1152c, {12,4,6}*1152c, {12,6,4}*1152a, {12,6,6}*1152a, {6,12,2}*1152b, {12,6,2}*1152a, {12,6,2}*1152b, {12,12,2}*1152h, {6,4,6}*1152a, {6,4,6}*1152b, {6,4,12}*1152d, {6,6,4}*1152c, {6,6,12}*1152b, {6,12,4}*1152g, {6,12,4}*1152i, {6,12,6}*1152a, {12,4,6}*1152d, {12,6,4}*1152b, {6,12,2}*1152c, {6,24,2}*1152b, {6,6,2}*1152b, {6,24,2}*1152c, {6,24,2}*1152d, {24,6,2}*1152c, {6,6,8}*1152b, {6,6,12}*1152c, {6,8,6}*1152a, {6,8,6}*1152b, {6,12,6}*1152c, {6,24,2}*1152e, {12,6,2}*1152d, {24,6,2}*1152e, {6,6,6}*1152a, {6,6,8}*1152d, {6,8,6}*1152c, {6,8,6}*1152d, {6,6,4}*1152f, {6,12,4}*1152j, {6,12,2}*1152e, {6,12,2}*1152f, {12,12,2}*1152j, {12,12,2}*1152k
25-fold covers : {6,2,50}*1200, {6,50,2}*1200, {150,2,2}*1200, {6,10,2}*1200a, {6,10,2}*1200b, {6,10,10}*1200a, {6,10,10}*1200b, {6,10,10}*1200c, {30,10,2}*1200a, {30,2,10}*1200, {30,10,2}*1200b, {30,10,2}*1200c
26-fold covers : {12,2,26}*1248, {12,26,2}*1248, {6,2,52}*1248, {6,52,2}*1248a, {6,4,26}*1248, {6,26,4}*1248, {156,2,2}*1248, {78,2,4}*1248, {78,4,2}*1248a
27-fold covers : {162,2,2}*1296, {18,2,18}*1296, {18,18,2}*1296a, {18,18,2}*1296c, {6,6,18}*1296a, {18,6,6}*1296a, {6,18,2}*1296b, {18,6,2}*1296a, {18,6,2}*1296b, {6,2,54}*1296, {6,54,2}*1296a, {54,2,6}*1296, {54,6,2}*1296a, {54,6,2}*1296b, {6,6,6}*1296a, {6,6,6}*1296b, {6,6,2}*1296a, {6,6,2}*1296b, {18,6,2}*1296c, {18,6,2}*1296d, {6,18,2}*1296f, {18,6,2}*1296e, {18,6,2}*1296f, {6,6,2}*1296d, {6,18,2}*1296g, {6,18,2}*1296h, {18,6,2}*1296g, {6,6,18}*1296b, {6,6,18}*1296c, {6,6,18}*1296e, {6,18,6}*1296a, {6,18,6}*1296c, {18,6,6}*1296b, {18,6,6}*1296c, {18,6,6}*1296d, {18,6,6}*1296e, {6,18,2}*1296i, {18,6,2}*1296i, {6,6,6}*1296c, {6,6,6}*1296d, {6,6,6}*1296f, {6,6,6}*1296g, {6,6,6}*1296j, {6,6,6}*1296k, {6,6,6}*1296m, {6,6,6}*1296n, {6,6,6}*1296o, {6,6,6}*1296p, {6,6,2}*1296e, {6,6,2}*1296f, {6,6,2}*1296g, {6,6,6}*1296q, {6,6,6}*1296s, {6,6,6}*1296t
28-fold covers : {12,2,28}*1344, {12,14,4}*1344, {12,4,14}*1344, {6,4,28}*1344, {6,28,4}*1344, {24,2,14}*1344, {24,14,2}*1344, {6,2,56}*1344, {6,56,2}*1344, {6,8,14}*1344, {6,14,8}*1344, {12,28,2}*1344, {84,4,2}*1344a, {84,2,4}*1344, {42,4,4}*1344, {168,2,2}*1344, {42,2,8}*1344, {42,8,2}*1344, {6,4,14}*1344, {6,28,2}*1344, {42,4,2}*1344
29-fold covers : {6,2,58}*1392, {6,58,2}*1392, {174,2,2}*1392
30-fold covers : {36,2,10}*1440, {36,10,2}*1440, {18,2,20}*1440, {18,20,2}*1440a, {18,4,10}*1440, {18,10,4}*1440, {180,2,2}*1440, {90,2,4}*1440, {90,4,2}*1440a, {6,10,12}*1440, {6,12,10}*1440a, {12,6,10}*1440a, {12,6,10}*1440b, {12,10,6}*1440, {6,6,20}*1440a, {6,20,6}*1440, {6,6,20}*1440c, {6,60,2}*1440a, {12,30,2}*1440a, {6,12,10}*1440c, {6,30,4}*1440a, {12,2,30}*1440, {12,30,2}*1440b, {30,2,12}*1440, {30,12,2}*1440b, {6,2,60}*1440, {6,60,2}*1440b, {60,2,6}*1440, {60,6,2}*1440b, {60,6,2}*1440c, {6,4,30}*1440, {6,30,4}*1440b, {30,4,6}*1440, {30,6,4}*1440b, {30,6,4}*1440c, {30,12,2}*1440c
31-fold covers : {6,2,62}*1488, {6,62,2}*1488, {186,2,2}*1488
33-fold covers : {18,2,22}*1584, {18,22,2}*1584, {198,2,2}*1584, {6,6,22}*1584a, {6,6,22}*1584c, {6,22,6}*1584, {6,66,2}*1584a, {6,2,66}*1584, {6,66,2}*1584b, {66,2,6}*1584, {66,6,2}*1584b, {66,6,2}*1584c
34-fold covers : {12,2,34}*1632, {12,34,2}*1632, {6,2,68}*1632, {6,68,2}*1632a, {6,4,34}*1632, {6,34,4}*1632, {204,2,2}*1632, {102,2,4}*1632, {102,4,2}*1632a
35-fold covers : {6,10,14}*1680, {6,14,10}*1680, {30,2,14}*1680, {30,14,2}*1680, {42,2,10}*1680, {42,10,2}*1680, {6,2,70}*1680, {6,70,2}*1680, {210,2,2}*1680
36-fold covers : {108,4,2}*1728a, {108,2,4}*1728, {54,4,4}*1728, {216,2,2}*1728, {54,2,8}*1728, {54,8,2}*1728, {12,2,36}*1728, {36,2,12}*1728, {12,6,12}*1728a, {36,6,4}*1728a, {12,18,4}*1728a, {12,4,18}*1728, {18,4,12}*1728, {18,12,4}*1728a, {6,4,36}*1728, {6,36,4}*1728a, {36,4,6}*1728, {12,6,4}*1728a, {6,12,4}*1728b, {6,12,12}*1728a, {12,12,6}*1728a, {6,2,72}*1728, {6,72,2}*1728a, {72,2,6}*1728, {72,6,2}*1728a, {72,6,2}*1728b, {18,2,24}*1728, {18,24,2}*1728a, {24,2,18}*1728, {24,18,2}*1728a, {6,6,24}*1728a, {24,6,6}*1728a, {6,24,2}*1728b, {24,6,2}*1728a, {24,6,2}*1728b, {6,8,18}*1728, {6,18,8}*1728a, {18,6,8}*1728a, {18,8,6}*1728, {6,6,8}*1728b, {6,24,6}*1728a, {12,36,2}*1728a, {36,12,2}*1728a, {36,12,2}*1728b, {36,6,4}*1728b, {12,12,2}*1728a, {12,12,2}*1728c, {12,6,4}*1728b, {18,6,8}*1728b, {18,24,2}*1728b, {6,6,8}*1728c, {6,24,2}*1728c, {18,12,4}*1728b, {6,12,4}*1728c, {54,4,2}*1728, {6,6,24}*1728b, {6,6,24}*1728c, {6,24,6}*1728b, {6,24,6}*1728d, {24,6,6}*1728b, {24,6,6}*1728c, {24,6,6}*1728d, {6,6,24}*1728e, {24,6,6}*1728e, {6,24,2}*1728f, {24,6,2}*1728f, {12,6,12}*1728b, {12,6,12}*1728d, {12,6,12}*1728e, {12,6,12}*1728f, {6,12,12}*1728b, {6,12,12}*1728c, {6,12,12}*1728e, {12,12,6}*1728b, {12,12,6}*1728d, {12,12,6}*1728f, {6,6,8}*1728e, {6,6,24}*1728f, {6,24,6}*1728f, {6,24,6}*1728g, {12,12,2}*1728h, {6,12,4}*1728j, {6,12,12}*1728g, {12,12,6}*1728g, {12,6,4}*1728h, {6,4,18}*1728a, {18,4,6}*1728a, {18,6,4}*1728, {18,6,6}*1728, {6,36,2}*1728, {18,6,2}*1728, {36,6,2}*1728, {6,4,18}*1728b, {6,18,4}*1728a, {18,4,6}*1728b, {12,18,2}*1728a, {18,12,2}*1728a, {18,12,2}*1728b, {6,6,4}*1728b, {6,12,6}*1728a, {6,12,6}*1728b, {6,6,2}*1728a, {6,12,2}*1728a, {6,12,2}*1728b, {12,6,2}*1728b, {6,6,8}*1728f, {6,8,6}*1728b, {12,4,4}*1728b, {12,6,4}*1728k, {12,6,4}*1728l, {12,4,6}*1728a, {12,4,2}*1728c, {12,4,2}*1728d, {6,6,8}*1728g, {6,8,2}*1728b, {6,4,4}*1728b, {6,4,4}*1728c, {6,4,12}*1728b, {6,12,4}*1728n, {6,12,4}*1728p, {12,4,4}*1728c, {24,6,2}*1728h, {12,6,4}*1728n, {12,12,2}*1728k, {6,6,4}*1728c, {6,6,6}*1728a, {6,6,6}*1728b, {6,6,6}*1728f, {6,6,12}*1728a, {6,6,12}*1728c, {6,12,6}*1728e, {6,12,6}*1728f, {6,12,6}*1728h, {6,12,6}*1728i, {6,12,6}*1728j, {6,12,6}*1728k, {6,12,6}*1728l, {12,6,6}*1728a, {12,6,6}*1728c, {6,6,2}*1728c, {6,12,2}*1728c, {12,6,2}*1728c
37-fold covers : {6,2,74}*1776, {6,74,2}*1776, {222,2,2}*1776
38-fold covers : {12,2,38}*1824, {12,38,2}*1824, {6,2,76}*1824, {6,76,2}*1824a, {6,4,38}*1824, {6,38,4}*1824, {228,2,2}*1824, {114,2,4}*1824, {114,4,2}*1824a
39-fold covers : {18,2,26}*1872, {18,26,2}*1872, {234,2,2}*1872, {6,6,26}*1872a, {6,6,26}*1872c, {6,26,6}*1872, {6,78,2}*1872a, {6,2,78}*1872, {6,78,2}*1872b, {78,2,6}*1872, {78,6,2}*1872b, {78,6,2}*1872c
40-fold covers : {60,4,4}*1920, {12,20,4}*1920, {12,4,20}*1920, {30,4,8}*1920a, {30,8,4}*1920a, {60,8,2}*1920a, {120,4,2}*1920a, {12,8,10}*1920a, {6,8,20}*1920a, {6,20,8}*1920a, {24,4,10}*1920a, {6,4,40}*1920a, {6,40,4}*1920a, {12,40,2}*1920a, {24,20,2}*1920a, {30,4,8}*1920b, {30,8,4}*1920b, {60,8,2}*1920b, {120,4,2}*1920b, {12,8,10}*1920b, {6,8,20}*1920b, {6,20,8}*1920b, {24,4,10}*1920b, {6,4,40}*1920b, {6,40,4}*1920b, {12,40,2}*1920b, {24,20,2}*1920b, {30,4,4}*1920a, {60,4,2}*1920a, {12,4,10}*1920a, {6,4,20}*1920a, {6,20,4}*1920a, {12,20,2}*1920a, {60,2,8}*1920, {120,2,4}*1920, {12,10,8}*1920, {24,10,4}*1920, {12,2,40}*1920, {24,2,20}*1920, {30,2,16}*1920, {30,16,2}*1920, {240,2,2}*1920, {6,10,16}*1920, {6,16,10}*1920, {48,2,10}*1920, {48,10,2}*1920, {6,2,80}*1920, {6,80,2}*1920, {12,4,10}*1920b, {12,20,2}*1920b, {6,4,20}*1920b, {6,20,2}*1920a, {6,4,10}*1920, {6,20,4}*1920c, {12,4,10}*1920c, {6,40,2}*1920b, {6,8,10}*1920a, {6,40,2}*1920c, {6,8,10}*1920b, {12,20,2}*1920c, {60,4,2}*1920b, {30,4,4}*1920d, {30,4,2}*1920b, {60,4,2}*1920c, {30,8,2}*1920b, {30,8,2}*1920c
41-fold covers : {6,2,82}*1968, {6,82,2}*1968, {246,2,2}*1968
Permutation Representation (GAP) :
s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := (7,8);;
s3 := ( 9,10);;
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*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(10)!(3,4)(5,6);
s1 := Sym(10)!(1,5)(2,3)(4,6);
s2 := Sym(10)!(7,8);
s3 := Sym(10)!( 9,10);
poly := sub<Sym(10)|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*s0*s1*s0*s1 >;
to this polytope