Polytope of Type {2,2,6}

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

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 7, 8)( 9,10);;
s3 := ( 5, 9)( 6, 7)( 8,10);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(10)!(1,2);
s1 := Sym(10)!(3,4);
s2 := Sym(10)!( 7, 8)( 9,10);
s3 := Sym(10)!( 5, 9)( 6, 7)( 8,10);
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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope