Polytope of Type {2,6,2}

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

s0 := (1,2);;
s1 := (5,6)(7,8);;
s2 := (3,7)(4,5)(6,8);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(10)!(1,2);
s1 := Sym(10)!(5,6)(7,8);
s2 := Sym(10)!(3,7)(4,5)(6,8);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope