Polytope of Type {2,2,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,3,2}*48
if this polytope has a name.
Group : SmallGroup(48,51)
Rank : 5
Schlafli Type : {2,2,3,2}
Number of vertices, edges, etc : 2, 2, 3, 3, 2
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,3,2,2} of size 96
   {2,2,3,2,3} of size 144
   {2,2,3,2,4} of size 192
   {2,2,3,2,5} of size 240
   {2,2,3,2,6} of size 288
   {2,2,3,2,7} of size 336
   {2,2,3,2,8} of size 384
   {2,2,3,2,9} of size 432
   {2,2,3,2,10} of size 480
   {2,2,3,2,11} of size 528
   {2,2,3,2,12} of size 576
   {2,2,3,2,13} of size 624
   {2,2,3,2,14} of size 672
   {2,2,3,2,15} of size 720
   {2,2,3,2,16} of size 768
   {2,2,3,2,17} of size 816
   {2,2,3,2,18} of size 864
   {2,2,3,2,19} of size 912
   {2,2,3,2,20} of size 960
   {2,2,3,2,21} of size 1008
   {2,2,3,2,22} of size 1056
   {2,2,3,2,23} of size 1104
   {2,2,3,2,24} of size 1152
   {2,2,3,2,25} of size 1200
   {2,2,3,2,26} of size 1248
   {2,2,3,2,27} of size 1296
   {2,2,3,2,28} of size 1344
   {2,2,3,2,29} of size 1392
   {2,2,3,2,30} of size 1440
   {2,2,3,2,31} of size 1488
   {2,2,3,2,33} of size 1584
   {2,2,3,2,34} of size 1632
   {2,2,3,2,35} of size 1680
   {2,2,3,2,36} of size 1728
   {2,2,3,2,37} of size 1776
   {2,2,3,2,38} of size 1824
   {2,2,3,2,39} of size 1872
   {2,2,3,2,40} of size 1920
   {2,2,3,2,41} of size 1968
Vertex Figure Of :
   {2,2,2,3,2} of size 96
   {3,2,2,3,2} of size 144
   {4,2,2,3,2} of size 192
   {5,2,2,3,2} of size 240
   {6,2,2,3,2} of size 288
   {7,2,2,3,2} of size 336
   {8,2,2,3,2} of size 384
   {9,2,2,3,2} of size 432
   {10,2,2,3,2} of size 480
   {11,2,2,3,2} of size 528
   {12,2,2,3,2} of size 576
   {13,2,2,3,2} of size 624
   {14,2,2,3,2} of size 672
   {15,2,2,3,2} of size 720
   {16,2,2,3,2} of size 768
   {17,2,2,3,2} of size 816
   {18,2,2,3,2} of size 864
   {19,2,2,3,2} of size 912
   {20,2,2,3,2} of size 960
   {21,2,2,3,2} of size 1008
   {22,2,2,3,2} of size 1056
   {23,2,2,3,2} of size 1104
   {24,2,2,3,2} of size 1152
   {25,2,2,3,2} of size 1200
   {26,2,2,3,2} of size 1248
   {27,2,2,3,2} of size 1296
   {28,2,2,3,2} of size 1344
   {29,2,2,3,2} of size 1392
   {30,2,2,3,2} of size 1440
   {31,2,2,3,2} of size 1488
   {33,2,2,3,2} of size 1584
   {34,2,2,3,2} of size 1632
   {35,2,2,3,2} of size 1680
   {36,2,2,3,2} of size 1728
   {37,2,2,3,2} of size 1776
   {38,2,2,3,2} of size 1824
   {39,2,2,3,2} of size 1872
   {40,2,2,3,2} of size 1920
   {41,2,2,3,2} of size 1968
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,3,2}*96, {2,2,6,2}*96
   3-fold covers : {2,2,9,2}*144, {2,2,3,6}*144, {2,6,3,2}*144, {6,2,3,2}*144
   4-fold covers : {8,2,3,2}*192, {2,2,12,2}*192, {2,2,6,4}*192a, {2,4,6,2}*192a, {4,2,6,2}*192, {2,2,3,4}*192, {2,4,3,2}*192
   5-fold covers : {10,2,3,2}*240, {2,2,15,2}*240
   6-fold covers : {4,2,9,2}*288, {2,2,18,2}*288, {12,2,3,2}*288, {4,2,3,6}*288, {4,6,3,2}*288, {2,2,6,6}*288a, {2,2,6,6}*288c, {2,6,6,2}*288a, {2,6,6,2}*288b, {6,2,6,2}*288
   7-fold covers : {14,2,3,2}*336, {2,2,21,2}*336
   8-fold covers : {16,2,3,2}*384, {2,2,12,4}*384a, {2,4,12,2}*384a, {4,2,12,2}*384, {4,4,6,2}*384, {2,4,6,4}*384a, {4,2,6,4}*384a, {2,2,24,2}*384, {2,2,6,8}*384, {2,8,6,2}*384, {8,2,6,2}*384, {4,2,3,4}*384, {4,4,3,2}*384b, {2,2,3,8}*384, {2,8,3,2}*384, {2,2,6,4}*384, {2,4,6,2}*384
   9-fold covers : {2,2,27,2}*432, {2,2,9,6}*432, {2,6,9,2}*432, {6,2,9,2}*432, {18,2,3,2}*432, {2,2,3,6}*432, {2,6,3,2}*432, {6,6,3,2}*432a, {2,6,3,6}*432, {6,2,3,6}*432, {6,6,3,2}*432b
   10-fold covers : {20,2,3,2}*480, {4,2,15,2}*480, {2,2,6,10}*480, {2,10,6,2}*480, {10,2,6,2}*480, {2,2,30,2}*480
   11-fold covers : {22,2,3,2}*528, {2,2,33,2}*528
   12-fold covers : {8,2,9,2}*576, {2,2,36,2}*576, {2,2,18,4}*576a, {2,4,18,2}*576a, {4,2,18,2}*576, {24,2,3,2}*576, {8,2,3,6}*576, {8,6,3,2}*576, {2,2,9,4}*576, {2,4,9,2}*576, {2,2,6,12}*576a, {2,2,12,6}*576a, {2,2,12,6}*576b, {2,6,12,2}*576a, {2,6,12,2}*576b, {2,12,6,2}*576a, {6,2,12,2}*576, {12,2,6,2}*576, {2,4,6,6}*576a, {2,4,6,6}*576b, {2,6,6,4}*576a, {2,6,6,4}*576b, {4,2,6,6}*576a, {4,2,6,6}*576c, {4,6,6,2}*576a, {6,2,6,4}*576a, {6,4,6,2}*576, {2,2,6,12}*576c, {2,12,6,2}*576c, {4,6,6,2}*576c, {2,2,3,6}*576, {2,2,3,12}*576, {2,4,3,6}*576, {2,6,3,2}*576, {2,6,3,4}*576, {2,12,3,2}*576, {6,2,3,4}*576, {6,4,3,2}*576
   13-fold covers : {26,2,3,2}*624, {2,2,39,2}*624
   14-fold covers : {28,2,3,2}*672, {4,2,21,2}*672, {2,2,6,14}*672, {2,14,6,2}*672, {14,2,6,2}*672, {2,2,42,2}*672
   15-fold covers : {10,2,9,2}*720, {2,2,45,2}*720, {10,2,3,6}*720, {10,6,3,2}*720, {2,2,15,6}*720, {2,6,15,2}*720, {6,2,15,2}*720, {30,2,3,2}*720
   16-fold covers : {32,2,3,2}*768, {4,4,12,2}*768, {2,4,12,4}*768a, {4,4,6,4}*768a, {4,2,12,4}*768a, {4,8,6,2}*768a, {8,4,6,2}*768a, {2,2,12,8}*768a, {2,8,12,2}*768a, {2,2,24,4}*768a, {2,4,24,2}*768a, {4,8,6,2}*768b, {8,4,6,2}*768b, {2,2,12,8}*768b, {2,8,12,2}*768b, {2,2,24,4}*768b, {2,4,24,2}*768b, {4,4,6,2}*768a, {2,2,12,4}*768a, {2,4,12,2}*768a, {4,2,6,8}*768, {8,2,6,4}*768a, {2,4,6,8}*768a, {2,8,6,4}*768a, {8,2,12,2}*768, {4,2,24,2}*768, {2,2,6,16}*768, {2,16,6,2}*768, {16,2,6,2}*768, {2,2,48,2}*768, {2,2,3,8}*768, {2,8,3,2}*768, {4,4,3,2}*768b, {4,8,3,2}*768, {8,2,3,4}*768, {8,4,3,2}*768, {4,2,3,8}*768, {2,2,12,4}*768b, {2,4,12,2}*768b, {2,2,6,4}*768b, {2,2,12,4}*768c, {2,4,6,2}*768b, {2,4,6,4}*768a, {2,4,6,4}*768b, {2,4,12,2}*768c, {4,2,6,4}*768, {4,4,6,2}*768d, {2,2,6,8}*768b, {2,8,6,2}*768b, {2,2,6,8}*768c, {2,8,6,2}*768c, {2,4,3,4}*768
   17-fold covers : {34,2,3,2}*816, {2,2,51,2}*816
   18-fold covers : {4,2,27,2}*864, {2,2,54,2}*864, {36,2,3,2}*864, {12,2,9,2}*864, {12,6,3,2}*864a, {4,2,9,6}*864, {4,2,3,6}*864, {4,6,9,2}*864, {4,6,3,2}*864a, {2,2,6,18}*864a, {2,2,18,6}*864a, {2,2,18,6}*864b, {2,6,18,2}*864a, {2,6,18,2}*864b, {2,18,6,2}*864a, {6,2,18,2}*864, {18,2,6,2}*864, {2,2,6,6}*864b, {2,2,6,6}*864c, {2,6,6,2}*864a, {2,6,6,2}*864b, {6,6,6,2}*864a, {12,2,3,6}*864, {12,6,3,2}*864b, {4,6,3,6}*864, {4,6,3,2}*864b, {2,2,6,6}*864d, {2,6,6,2}*864d, {2,6,6,6}*864b, {2,6,6,6}*864d, {2,6,6,6}*864e, {2,6,6,6}*864f, {6,2,6,6}*864a, {6,2,6,6}*864c, {6,6,6,2}*864b, {6,6,6,2}*864c, {6,6,6,2}*864d, {6,6,6,2}*864g
   19-fold covers : {38,2,3,2}*912, {2,2,57,2}*912
   20-fold covers : {40,2,3,2}*960, {8,2,15,2}*960, {2,2,12,10}*960, {2,10,12,2}*960, {10,2,12,2}*960, {2,2,6,20}*960a, {2,20,6,2}*960a, {20,2,6,2}*960, {2,4,6,10}*960a, {2,10,6,4}*960a, {4,2,6,10}*960, {4,10,6,2}*960, {10,2,6,4}*960a, {10,4,6,2}*960, {2,2,60,2}*960, {2,2,30,4}*960a, {2,4,30,2}*960a, {4,2,30,2}*960, {10,2,3,4}*960, {10,4,3,2}*960, {2,2,15,4}*960, {2,4,15,2}*960
   21-fold covers : {14,2,9,2}*1008, {2,2,63,2}*1008, {14,2,3,6}*1008, {14,6,3,2}*1008, {2,2,21,6}*1008, {2,6,21,2}*1008, {6,2,21,2}*1008, {42,2,3,2}*1008
   22-fold covers : {44,2,3,2}*1056, {4,2,33,2}*1056, {2,2,6,22}*1056, {2,22,6,2}*1056, {22,2,6,2}*1056, {2,2,66,2}*1056
   23-fold covers : {46,2,3,2}*1104, {2,2,69,2}*1104
   24-fold covers : {16,2,9,2}*1152, {16,2,3,6}*1152, {16,6,3,2}*1152, {48,2,3,2}*1152, {4,4,18,2}*1152, {2,2,36,4}*1152a, {2,4,36,2}*1152a, {4,4,6,6}*1152a, {4,4,6,6}*1152b, {2,4,12,6}*1152a, {2,4,12,6}*1152b, {2,6,12,4}*1152a, {2,6,12,4}*1152b, {4,12,6,2}*1152a, {6,2,12,4}*1152a, {6,4,12,2}*1152, {12,4,6,2}*1152, {4,12,6,2}*1152c, {2,2,12,12}*1152a, {2,2,12,12}*1152c, {2,12,12,2}*1152a, {2,12,12,2}*1152b, {4,2,18,4}*1152a, {2,4,18,4}*1152a, {4,2,36,2}*1152, {6,4,6,4}*1152a, {4,6,6,4}*1152a, {4,6,6,4}*1152c, {4,2,6,12}*1152a, {4,2,6,12}*1152b, {4,2,12,6}*1152b, {4,2,12,6}*1152c, {12,2,6,4}*1152a, {2,4,6,12}*1152a, {2,12,6,4}*1152a, {2,4,6,12}*1152b, {2,12,6,4}*1152b, {4,6,12,2}*1152b, {4,6,12,2}*1152c, {12,2,12,2}*1152, {2,2,18,8}*1152, {2,8,18,2}*1152, {8,2,18,2}*1152, {2,2,72,2}*1152, {2,6,6,8}*1152a, {2,6,6,8}*1152b, {2,8,6,6}*1152a, {2,8,6,6}*1152b, {6,2,6,8}*1152, {6,8,6,2}*1152, {8,2,6,6}*1152a, {8,2,6,6}*1152c, {8,6,6,2}*1152a, {2,2,6,24}*1152a, {2,24,6,2}*1152a, {8,6,6,2}*1152c, {2,2,6,24}*1152b, {2,2,24,6}*1152b, {2,2,24,6}*1152c, {2,6,24,2}*1152b, {2,6,24,2}*1152c, {2,24,6,2}*1152b, {6,2,24,2}*1152, {24,2,6,2}*1152, {4,2,9,4}*1152, {4,4,9,2}*1152b, {2,2,9,8}*1152, {2,8,9,2}*1152, {2,2,18,4}*1152, {2,4,18,2}*1152, {12,2,3,4}*1152, {12,4,3,2}*1152, {4,4,3,6}*1152b, {4,2,3,6}*1152, {4,2,3,12}*1152, {2,2,3,12}*1152, {2,2,3,24}*1152, {2,12,3,2}*1152, {2,24,3,2}*1152, {2,6,3,8}*1152, {2,8,3,6}*1152, {6,2,3,8}*1152, {6,8,3,2}*1152, {4,6,3,4}*1152, {4,6,3,2}*1152a, {4,12,3,2}*1152, {2,2,6,6}*1152b, {2,2,6,12}*1152a, {2,2,6,12}*1152b, {2,2,12,6}*1152a, {2,4,6,6}*1152a, {2,4,6,6}*1152b, {2,6,6,2}*1152a, {2,6,6,4}*1152a, {2,6,6,4}*1152b, {2,6,12,2}*1152a, {2,12,6,2}*1152a, {2,12,6,2}*1152b, {4,6,6,2}*1152a, {6,2,6,4}*1152, {6,4,6,2}*1152a, {6,4,6,2}*1152b, {6,6,6,2}*1152b
   25-fold covers : {50,2,3,2}*1200, {2,2,75,2}*1200, {2,2,3,10}*1200, {2,10,3,2}*1200, {2,2,15,10}*1200, {2,10,15,2}*1200, {10,2,15,2}*1200
   26-fold covers : {52,2,3,2}*1248, {4,2,39,2}*1248, {2,2,6,26}*1248, {2,26,6,2}*1248, {26,2,6,2}*1248, {2,2,78,2}*1248
   27-fold covers : {2,2,81,2}*1296, {2,2,9,18}*1296, {2,18,9,2}*1296, {18,2,9,2}*1296, {2,2,9,6}*1296a, {2,6,9,2}*1296a, {6,6,9,2}*1296a, {18,6,3,2}*1296a, {2,2,27,6}*1296, {2,6,27,2}*1296, {6,2,27,2}*1296, {54,2,3,2}*1296, {2,2,9,6}*1296b, {2,2,9,6}*1296c, {2,6,9,2}*1296b, {2,6,9,2}*1296c, {6,6,3,2}*1296a, {6,6,3,2}*1296b, {2,2,9,6}*1296d, {2,6,9,2}*1296d, {2,2,3,6}*1296, {2,2,3,18}*1296, {2,6,3,2}*1296, {2,18,3,2}*1296, {2,6,9,6}*1296, {6,2,9,6}*1296, {6,6,9,2}*1296b, {18,2,3,6}*1296, {18,6,3,2}*1296b, {6,6,3,6}*1296a, {2,6,3,6}*1296a, {2,6,3,6}*1296b, {6,2,3,6}*1296, {6,6,3,2}*1296c, {6,6,3,2}*1296d, {6,6,3,2}*1296e, {6,6,3,6}*1296b
   28-fold covers : {56,2,3,2}*1344, {8,2,21,2}*1344, {2,2,12,14}*1344, {2,14,12,2}*1344, {14,2,12,2}*1344, {2,2,6,28}*1344a, {2,28,6,2}*1344a, {28,2,6,2}*1344, {2,4,6,14}*1344a, {2,14,6,4}*1344a, {4,2,6,14}*1344, {4,14,6,2}*1344, {14,2,6,4}*1344a, {14,4,6,2}*1344, {2,2,84,2}*1344, {2,2,42,4}*1344a, {2,4,42,2}*1344a, {4,2,42,2}*1344, {14,2,3,4}*1344, {14,4,3,2}*1344, {2,2,21,4}*1344, {2,4,21,2}*1344
   29-fold covers : {58,2,3,2}*1392, {2,2,87,2}*1392
   30-fold covers : {20,2,9,2}*1440, {4,2,45,2}*1440, {2,2,18,10}*1440, {2,10,18,2}*1440, {10,2,18,2}*1440, {2,2,90,2}*1440, {20,2,3,6}*1440, {20,6,3,2}*1440, {12,2,15,2}*1440, {60,2,3,2}*1440, {4,2,15,6}*1440, {4,6,15,2}*1440, {2,2,6,30}*1440a, {2,6,6,10}*1440a, {2,6,6,10}*1440b, {2,10,6,6}*1440a, {2,10,6,6}*1440c, {2,30,6,2}*1440a, {6,2,6,10}*1440, {6,10,6,2}*1440, {10,2,6,6}*1440a, {10,2,6,6}*1440c, {10,6,6,2}*1440a, {10,6,6,2}*1440b, {2,2,6,30}*1440b, {2,2,30,6}*1440b, {2,2,30,6}*1440c, {2,6,30,2}*1440b, {2,6,30,2}*1440c, {2,30,6,2}*1440b, {6,2,30,2}*1440, {30,2,6,2}*1440
   31-fold covers : {62,2,3,2}*1488, {2,2,93,2}*1488
   33-fold covers : {22,2,9,2}*1584, {2,2,99,2}*1584, {22,2,3,6}*1584, {22,6,3,2}*1584, {2,2,33,6}*1584, {2,6,33,2}*1584, {6,2,33,2}*1584, {66,2,3,2}*1584
   34-fold covers : {68,2,3,2}*1632, {4,2,51,2}*1632, {2,2,6,34}*1632, {2,34,6,2}*1632, {34,2,6,2}*1632, {2,2,102,2}*1632
   35-fold covers : {14,2,15,2}*1680, {10,2,21,2}*1680, {70,2,3,2}*1680, {2,2,105,2}*1680
   36-fold covers : {8,2,27,2}*1728, {2,2,108,2}*1728, {2,2,54,4}*1728a, {2,4,54,2}*1728a, {4,2,54,2}*1728, {72,2,3,2}*1728, {24,2,9,2}*1728, {24,6,3,2}*1728a, {8,2,9,6}*1728, {8,2,3,6}*1728, {8,6,9,2}*1728, {8,6,3,2}*1728a, {2,2,27,4}*1728, {2,4,27,2}*1728, {2,2,12,18}*1728a, {2,2,18,12}*1728a, {2,12,18,2}*1728a, {2,18,12,2}*1728a, {12,2,18,2}*1728, {18,2,12,2}*1728, {2,2,6,36}*1728a, {2,2,36,6}*1728a, {2,2,36,6}*1728b, {2,6,36,2}*1728a, {2,6,36,2}*1728b, {2,36,6,2}*1728a, {6,2,36,2}*1728, {36,2,6,2}*1728, {2,2,6,12}*1728b, {2,2,12,6}*1728a, {2,2,12,6}*1728b, {2,6,12,2}*1728a, {2,6,12,2}*1728b, {2,12,6,2}*1728b, {6,6,12,2}*1728a, {12,6,6,2}*1728a, {2,4,6,18}*1728a, {2,4,18,6}*1728a, {2,4,18,6}*1728b, {2,6,18,4}*1728a, {2,6,18,4}*1728b, {2,18,6,4}*1728a, {4,2,6,18}*1728a, {4,2,18,6}*1728a, {4,2,18,6}*1728b, {4,6,18,2}*1728a, {4,18,6,2}*1728a, {6,2,18,4}*1728a, {6,4,18,2}*1728, {18,2,6,4}*1728a, {18,4,6,2}*1728, {6,6,6,4}*1728a, {2,4,6,6}*1728a, {2,4,6,6}*1728b, {2,6,6,4}*1728a, {2,6,6,4}*1728b, {4,2,6,6}*1728b, {4,2,6,6}*1728c, {4,6,6,2}*1728b, {6,12,6,2}*1728a, {2,2,18,12}*1728b, {2,12,18,2}*1728b, {4,6,18,2}*1728b, {2,2,6,12}*1728c, {2,12,6,2}*1728c, {4,6,6,2}*1728c, {24,2,3,6}*1728, {24,6,3,2}*1728b, {8,6,3,6}*1728, {2,2,9,6}*1728, {2,6,9,2}*1728, {18,2,3,4}*1728, {18,4,3,2}*1728, {2,2,9,12}*1728, {2,4,9,6}*1728, {2,6,9,4}*1728, {2,12,9,2}*1728, {6,2,9,4}*1728, {6,4,9,2}*1728, {2,2,3,6}*1728, {2,2,3,12}*1728, {6,6,3,4}*1728a, {2,4,3,6}*1728, {2,6,3,2}*1728, {2,6,3,4}*1728, {2,12,3,2}*1728, {6,12,3,2}*1728a, {8,6,3,2}*1728b, {2,6,6,12}*1728b, {2,6,6,12}*1728d, {2,6,12,6}*1728b, {2,6,12,6}*1728c, {2,6,12,6}*1728d, {2,6,12,6}*1728e, {2,12,6,6}*1728b, {2,12,6,6}*1728c, {6,2,6,12}*1728a, {6,2,12,6}*1728a, {6,2,12,6}*1728b, {6,6,12,2}*1728b, {6,6,12,2}*1728c, {6,6,12,2}*1728d, {6,12,6,2}*1728b, {6,12,6,2}*1728c, {12,2,6,6}*1728a, {12,2,6,6}*1728c, {12,6,6,2}*1728b, {12,6,6,2}*1728d, {4,6,6,6}*1728d, {4,6,6,6}*1728e, {6,4,6,6}*1728a, {6,4,6,6}*1728b, {6,6,6,4}*1728d, {6,6,6,4}*1728e, {6,6,6,4}*1728f, {4,2,6,6}*1728d, {2,2,6,12}*1728g, {2,2,12,6}*1728g, {2,6,12,2}*1728g, {2,12,6,2}*1728g, {6,6,12,2}*1728e, {12,6,6,2}*1728e, {4,6,6,6}*1728g, {4,6,6,6}*1728h, {2,4,6,6}*1728h, {2,6,6,4}*1728h, {2,6,6,12}*1728f, {2,6,6,12}*1728g, {2,12,6,6}*1728f, {2,12,6,6}*1728g, {4,6,6,2}*1728h, {6,2,6,12}*1728c, {6,12,6,2}*1728f, {6,12,6,2}*1728g, {12,6,6,2}*1728f, {6,6,6,4}*1728i, {6,4,3,6}*1728, {6,6,3,4}*1728b, {2,6,3,6}*1728a, {2,6,3,6}*1728b, {2,6,3,12}*1728, {2,12,3,6}*1728, {6,2,3,6}*1728, {6,2,3,12}*1728, {6,6,3,2}*1728, {6,12,3,2}*1728b, {2,2,6,4}*1728b, {2,2,12,4}*1728b, {2,4,6,2}*1728b, {2,4,12,2}*1728b, {4,4,6,2}*1728b, {4,6,6,2}*1728j, {4,6,6,2}*1728k, {6,4,6,2}*1728b, {2,2,12,6}*1728i, {2,6,12,2}*1728i
   37-fold covers : {74,2,3,2}*1776, {2,2,111,2}*1776
   38-fold covers : {76,2,3,2}*1824, {4,2,57,2}*1824, {2,2,6,38}*1824, {2,38,6,2}*1824, {38,2,6,2}*1824, {2,2,114,2}*1824
   39-fold covers : {26,2,9,2}*1872, {2,2,117,2}*1872, {26,2,3,6}*1872, {26,6,3,2}*1872, {2,2,39,6}*1872, {2,6,39,2}*1872, {6,2,39,2}*1872, {78,2,3,2}*1872
   40-fold covers : {16,2,15,2}*1920, {80,2,3,2}*1920, {4,4,30,2}*1920, {2,2,60,4}*1920a, {2,4,60,2}*1920a, {4,4,6,10}*1920, {2,4,12,10}*1920a, {2,10,12,4}*1920a, {10,2,12,4}*1920a, {10,4,12,2}*1920, {4,20,6,2}*1920, {20,4,6,2}*1920, {2,2,12,20}*1920, {2,20,12,2}*1920, {4,2,30,4}*1920a, {2,4,30,4}*1920a, {4,2,60,2}*1920, {10,4,6,4}*1920a, {4,10,6,4}*1920a, {4,2,12,10}*1920, {4,2,6,20}*1920a, {20,2,6,4}*1920a, {4,10,12,2}*1920, {2,4,6,20}*1920a, {2,20,6,4}*1920a, {20,2,12,2}*1920, {2,2,30,8}*1920, {2,8,30,2}*1920, {8,2,30,2}*1920, {2,2,120,2}*1920, {2,8,6,10}*1920, {2,10,6,8}*1920, {8,2,6,10}*1920, {8,10,6,2}*1920, {10,2,6,8}*1920, {10,8,6,2}*1920, {2,2,24,10}*1920, {2,10,24,2}*1920, {10,2,24,2}*1920, {2,2,6,40}*1920, {2,40,6,2}*1920, {40,2,6,2}*1920, {20,2,3,4}*1920, {20,4,3,2}*1920, {10,2,3,8}*1920, {10,8,3,2}*1920, {4,2,15,4}*1920, {4,4,15,2}*1920b, {2,2,15,8}*1920, {2,8,15,2}*1920, {2,2,6,20}*1920a, {2,4,6,10}*1920a, {2,10,6,4}*1920a, {2,20,6,2}*1920a, {10,2,6,4}*1920, {10,4,6,2}*1920, {2,2,30,4}*1920, {2,4,30,2}*1920
   41-fold covers : {82,2,3,2}*1968, {2,2,123,2}*1968
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (6,7);;
s3 := (5,6);;
s4 := (8,9);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(9)!(1,2);
s1 := Sym(9)!(3,4);
s2 := Sym(9)!(6,7);
s3 := Sym(9)!(5,6);
s4 := Sym(9)!(8,9);
poly := sub<Sym(9)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3 >;

to this polytope