Polytope of Type {2,2,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,2}*64
if this polytope has a name.
Group : SmallGroup(64,261)
Rank : 5
Schlafli Type : {2,2,4,2}
Number of vertices, edges, etc : 2, 2, 4, 4, 2
Order of s0s1s2s3s4 : 4
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,4,2,2} of size 128
   {2,2,4,2,3} of size 192
   {2,2,4,2,4} of size 256
   {2,2,4,2,5} of size 320
   {2,2,4,2,6} of size 384
   {2,2,4,2,7} of size 448
   {2,2,4,2,8} of size 512
   {2,2,4,2,9} of size 576
   {2,2,4,2,10} of size 640
   {2,2,4,2,11} of size 704
   {2,2,4,2,12} of size 768
   {2,2,4,2,13} of size 832
   {2,2,4,2,14} of size 896
   {2,2,4,2,15} of size 960
   {2,2,4,2,17} of size 1088
   {2,2,4,2,18} of size 1152
   {2,2,4,2,19} of size 1216
   {2,2,4,2,20} of size 1280
   {2,2,4,2,21} of size 1344
   {2,2,4,2,22} of size 1408
   {2,2,4,2,23} of size 1472
   {2,2,4,2,25} of size 1600
   {2,2,4,2,26} of size 1664
   {2,2,4,2,27} of size 1728
   {2,2,4,2,28} of size 1792
   {2,2,4,2,29} of size 1856
   {2,2,4,2,30} of size 1920
   {2,2,4,2,31} of size 1984
Vertex Figure Of :
   {2,2,2,4,2} of size 128
   {3,2,2,4,2} of size 192
   {4,2,2,4,2} of size 256
   {5,2,2,4,2} of size 320
   {6,2,2,4,2} of size 384
   {7,2,2,4,2} of size 448
   {8,2,2,4,2} of size 512
   {9,2,2,4,2} of size 576
   {10,2,2,4,2} of size 640
   {11,2,2,4,2} of size 704
   {12,2,2,4,2} of size 768
   {13,2,2,4,2} of size 832
   {14,2,2,4,2} of size 896
   {15,2,2,4,2} of size 960
   {17,2,2,4,2} of size 1088
   {18,2,2,4,2} of size 1152
   {19,2,2,4,2} of size 1216
   {20,2,2,4,2} of size 1280
   {21,2,2,4,2} of size 1344
   {22,2,2,4,2} of size 1408
   {23,2,2,4,2} of size 1472
   {25,2,2,4,2} of size 1600
   {26,2,2,4,2} of size 1664
   {27,2,2,4,2} of size 1728
   {28,2,2,4,2} of size 1792
   {29,2,2,4,2} of size 1856
   {30,2,2,4,2} of size 1920
   {31,2,2,4,2} of size 1984
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,4,4}*128, {2,4,4,2}*128, {4,2,4,2}*128, {2,2,8,2}*128
   3-fold covers : {2,2,12,2}*192, {2,2,4,6}*192a, {2,6,4,2}*192a, {6,2,4,2}*192
   4-fold covers : {2,4,4,4}*256, {4,4,4,2}*256, {4,2,4,4}*256, {2,2,4,8}*256a, {2,2,8,4}*256a, {2,4,8,2}*256a, {2,8,4,2}*256a, {2,2,4,8}*256b, {2,2,8,4}*256b, {2,4,8,2}*256b, {2,8,4,2}*256b, {2,2,4,4}*256, {2,4,4,2}*256, {4,2,8,2}*256, {8,2,4,2}*256, {2,2,16,2}*256
   5-fold covers : {2,2,20,2}*320, {2,2,4,10}*320, {2,10,4,2}*320, {10,2,4,2}*320
   6-fold covers : {2,2,4,12}*384a, {2,2,12,4}*384a, {2,4,12,2}*384a, {2,12,4,2}*384a, {4,2,12,2}*384, {12,2,4,2}*384, {2,4,4,6}*384, {2,6,4,4}*384, {6,2,4,4}*384, {6,4,4,2}*384, {4,6,4,2}*384a, {4,2,4,6}*384a, {2,2,24,2}*384, {2,2,8,6}*384, {2,6,8,2}*384, {6,2,8,2}*384
   7-fold covers : {2,2,28,2}*448, {2,2,4,14}*448, {2,14,4,2}*448, {14,2,4,2}*448
   8-fold covers : {4,4,4,4}*512, {2,2,4,8}*512a, {2,2,8,4}*512a, {2,4,8,2}*512a, {2,8,4,2}*512a, {2,2,8,8}*512a, {2,2,8,8}*512b, {2,2,8,8}*512c, {2,8,8,2}*512a, {2,8,8,2}*512b, {2,8,8,2}*512c, {2,2,8,8}*512d, {2,8,8,2}*512d, {8,2,8,2}*512, {2,4,8,4}*512a, {4,8,4,2}*512a, {2,4,8,4}*512b, {2,4,8,4}*512c, {4,8,4,2}*512b, {4,8,4,2}*512c, {2,4,8,4}*512d, {4,8,4,2}*512d, {2,4,4,8}*512a, {2,8,4,4}*512a, {4,4,8,2}*512a, {8,4,4,2}*512a, {2,4,4,8}*512b, {2,8,4,4}*512b, {4,4,8,2}*512b, {8,4,4,2}*512b, {2,4,4,4}*512a, {2,4,4,4}*512b, {4,4,4,2}*512a, {4,4,4,2}*512b, {2,2,4,16}*512a, {2,2,16,4}*512a, {2,4,16,2}*512a, {2,16,4,2}*512a, {2,2,4,16}*512b, {2,2,16,4}*512b, {2,4,16,2}*512b, {2,16,4,2}*512b, {2,2,4,4}*512, {2,2,4,8}*512b, {2,2,8,4}*512b, {2,4,4,2}*512, {2,4,8,2}*512b, {2,8,4,2}*512b, {4,2,16,2}*512, {16,2,4,2}*512, {2,2,32,2}*512
   9-fold covers : {2,2,36,2}*576, {2,2,4,18}*576a, {2,18,4,2}*576a, {18,2,4,2}*576, {2,2,12,6}*576a, {2,2,12,6}*576b, {2,6,12,2}*576a, {2,6,12,2}*576b, {6,2,12,2}*576, {2,6,4,6}*576, {6,2,4,6}*576a, {6,6,4,2}*576a, {6,6,4,2}*576b, {2,2,12,6}*576c, {2,6,12,2}*576c, {6,6,4,2}*576c, {2,2,4,6}*576, {2,6,4,2}*576
   10-fold covers : {2,2,4,20}*640, {2,2,20,4}*640, {2,4,20,2}*640, {2,20,4,2}*640, {4,2,20,2}*640, {20,2,4,2}*640, {2,4,4,10}*640, {2,10,4,4}*640, {10,2,4,4}*640, {10,4,4,2}*640, {4,10,4,2}*640, {4,2,4,10}*640, {2,2,40,2}*640, {2,2,8,10}*640, {2,10,8,2}*640, {10,2,8,2}*640
   11-fold covers : {2,2,44,2}*704, {2,2,4,22}*704, {2,22,4,2}*704, {22,2,4,2}*704
   12-fold covers : {4,4,4,6}*768, {6,4,4,4}*768, {2,4,4,12}*768, {2,12,4,4}*768, {4,4,12,2}*768, {12,4,4,2}*768, {2,4,12,4}*768a, {4,12,4,2}*768a, {4,6,4,4}*768a, {12,2,4,4}*768, {4,2,4,12}*768a, {4,2,12,4}*768a, {2,4,8,6}*768a, {2,6,4,8}*768a, {2,6,8,4}*768a, {2,8,4,6}*768a, {6,2,4,8}*768a, {6,2,8,4}*768a, {6,4,8,2}*768a, {6,8,4,2}*768a, {2,2,8,12}*768a, {2,2,12,8}*768a, {2,8,12,2}*768a, {2,12,8,2}*768a, {2,2,4,24}*768a, {2,2,24,4}*768a, {2,4,24,2}*768a, {2,24,4,2}*768a, {2,4,8,6}*768b, {2,6,4,8}*768b, {2,6,8,4}*768b, {2,8,4,6}*768b, {6,2,4,8}*768b, {6,2,8,4}*768b, {6,4,8,2}*768b, {6,8,4,2}*768b, {2,2,8,12}*768b, {2,2,12,8}*768b, {2,8,12,2}*768b, {2,12,8,2}*768b, {2,2,4,24}*768b, {2,2,24,4}*768b, {2,4,24,2}*768b, {2,24,4,2}*768b, {2,4,4,6}*768a, {2,6,4,4}*768a, {6,2,4,4}*768, {6,4,4,2}*768a, {2,2,4,12}*768a, {2,2,12,4}*768a, {2,4,12,2}*768a, {2,12,4,2}*768a, {4,2,8,6}*768, {8,2,4,6}*768a, {4,6,8,2}*768a, {8,6,4,2}*768a, {8,2,12,2}*768, {12,2,8,2}*768, {4,2,24,2}*768, {24,2,4,2}*768, {2,2,16,6}*768, {2,6,16,2}*768, {6,2,16,2}*768, {2,2,48,2}*768, {2,2,12,4}*768b, {2,4,12,2}*768b, {2,2,4,6}*768b, {2,2,12,6}*768a, {2,6,4,2}*768b, {2,6,12,2}*768a, {4,6,4,2}*768b, {6,4,4,2}*768d, {6,6,4,2}*768
   13-fold covers : {2,2,52,2}*832, {2,2,4,26}*832, {2,26,4,2}*832, {26,2,4,2}*832
   14-fold covers : {2,2,4,28}*896, {2,2,28,4}*896, {2,4,28,2}*896, {2,28,4,2}*896, {4,2,28,2}*896, {28,2,4,2}*896, {2,4,4,14}*896, {2,14,4,4}*896, {14,2,4,4}*896, {14,4,4,2}*896, {4,14,4,2}*896, {4,2,4,14}*896, {2,2,56,2}*896, {2,2,8,14}*896, {2,14,8,2}*896, {14,2,8,2}*896
   15-fold covers : {2,2,12,10}*960, {2,10,12,2}*960, {10,2,12,2}*960, {2,2,20,6}*960a, {2,6,20,2}*960a, {6,2,20,2}*960, {2,6,4,10}*960, {2,10,4,6}*960, {6,2,4,10}*960, {6,10,4,2}*960, {10,2,4,6}*960a, {10,6,4,2}*960a, {2,2,60,2}*960, {2,2,4,30}*960a, {2,30,4,2}*960a, {30,2,4,2}*960
   17-fold covers : {2,2,4,34}*1088, {2,34,4,2}*1088, {34,2,4,2}*1088, {2,2,68,2}*1088
   18-fold covers : {2,4,4,18}*1152, {2,18,4,4}*1152, {18,2,4,4}*1152, {18,4,4,2}*1152, {2,2,4,36}*1152a, {2,2,36,4}*1152a, {2,4,36,2}*1152a, {2,36,4,2}*1152a, {6,4,4,6}*1152, {6,6,4,4}*1152a, {6,6,4,4}*1152b, {6,6,4,4}*1152c, {2,4,12,6}*1152a, {2,4,12,6}*1152b, {2,6,4,12}*1152, {2,6,12,4}*1152a, {2,6,12,4}*1152b, {2,12,4,6}*1152, {6,2,4,12}*1152a, {6,2,12,4}*1152a, {6,4,12,2}*1152, {6,12,4,2}*1152a, {6,12,4,2}*1152b, {2,4,12,6}*1152c, {2,6,12,4}*1152c, {6,12,4,2}*1152c, {2,2,12,12}*1152a, {2,2,12,12}*1152b, {2,2,12,12}*1152c, {2,12,12,2}*1152a, {2,12,12,2}*1152b, {2,12,12,2}*1152c, {2,2,4,4}*1152, {2,2,4,12}*1152, {2,2,12,4}*1152, {2,4,4,2}*1152, {2,4,4,6}*1152, {2,4,12,2}*1152, {2,6,4,4}*1152, {2,12,4,2}*1152, {6,4,4,2}*1152, {4,2,4,18}*1152a, {4,18,4,2}*1152a, {4,2,36,2}*1152, {36,2,4,2}*1152, {4,6,4,6}*1152a, {4,2,12,6}*1152a, {4,2,12,6}*1152b, {4,2,12,6}*1152c, {12,2,4,6}*1152a, {4,6,12,2}*1152a, {12,6,4,2}*1152a, {4,6,12,2}*1152b, {12,6,4,2}*1152b, {4,6,12,2}*1152c, {12,6,4,2}*1152c, {12,2,12,2}*1152, {4,2,4,6}*1152, {4,4,4,2}*1152a, {4,6,4,2}*1152a, {4,6,4,2}*1152b, {2,2,8,18}*1152, {2,18,8,2}*1152, {18,2,8,2}*1152, {2,2,72,2}*1152, {2,6,8,6}*1152, {6,2,8,6}*1152, {6,6,8,2}*1152a, {6,6,8,2}*1152b, {2,2,24,6}*1152a, {2,6,24,2}*1152a, {6,6,8,2}*1152c, {2,2,24,6}*1152b, {2,2,24,6}*1152c, {2,6,24,2}*1152b, {2,6,24,2}*1152c, {6,2,24,2}*1152, {2,2,8,6}*1152, {2,6,8,2}*1152
   19-fold covers : {2,2,4,38}*1216, {2,38,4,2}*1216, {38,2,4,2}*1216, {2,2,76,2}*1216
   20-fold covers : {4,4,4,10}*1280, {10,4,4,4}*1280, {2,4,4,20}*1280, {2,20,4,4}*1280, {4,4,20,2}*1280, {20,4,4,2}*1280, {2,4,20,4}*1280, {4,20,4,2}*1280, {4,10,4,4}*1280, {20,2,4,4}*1280, {4,2,4,20}*1280, {4,2,20,4}*1280, {2,4,8,10}*1280a, {2,8,4,10}*1280a, {2,10,4,8}*1280a, {2,10,8,4}*1280a, {10,2,4,8}*1280a, {10,2,8,4}*1280a, {10,4,8,2}*1280a, {10,8,4,2}*1280a, {2,2,8,20}*1280a, {2,2,20,8}*1280a, {2,8,20,2}*1280a, {2,20,8,2}*1280a, {2,2,4,40}*1280a, {2,2,40,4}*1280a, {2,4,40,2}*1280a, {2,40,4,2}*1280a, {2,4,8,10}*1280b, {2,8,4,10}*1280b, {2,10,4,8}*1280b, {2,10,8,4}*1280b, {10,2,4,8}*1280b, {10,2,8,4}*1280b, {10,4,8,2}*1280b, {10,8,4,2}*1280b, {2,2,8,20}*1280b, {2,2,20,8}*1280b, {2,8,20,2}*1280b, {2,20,8,2}*1280b, {2,2,4,40}*1280b, {2,2,40,4}*1280b, {2,4,40,2}*1280b, {2,40,4,2}*1280b, {2,4,4,10}*1280, {2,10,4,4}*1280, {10,2,4,4}*1280, {10,4,4,2}*1280, {2,2,4,20}*1280, {2,2,20,4}*1280, {2,4,20,2}*1280, {2,20,4,2}*1280, {4,2,8,10}*1280, {8,2,4,10}*1280, {4,10,8,2}*1280, {8,10,4,2}*1280, {8,2,20,2}*1280, {20,2,8,2}*1280, {4,2,40,2}*1280, {40,2,4,2}*1280, {2,2,16,10}*1280, {2,10,16,2}*1280, {10,2,16,2}*1280, {2,2,80,2}*1280
   21-fold covers : {2,2,12,14}*1344, {2,14,12,2}*1344, {14,2,12,2}*1344, {2,2,28,6}*1344a, {2,6,28,2}*1344a, {6,2,28,2}*1344, {2,6,4,14}*1344, {2,14,4,6}*1344, {6,2,4,14}*1344, {6,14,4,2}*1344, {14,2,4,6}*1344a, {14,6,4,2}*1344a, {2,2,84,2}*1344, {2,2,4,42}*1344a, {2,42,4,2}*1344a, {42,2,4,2}*1344
   22-fold covers : {2,4,4,22}*1408, {2,22,4,4}*1408, {22,2,4,4}*1408, {22,4,4,2}*1408, {2,2,4,44}*1408, {2,2,44,4}*1408, {2,4,44,2}*1408, {2,44,4,2}*1408, {4,2,4,22}*1408, {4,22,4,2}*1408, {4,2,44,2}*1408, {44,2,4,2}*1408, {2,2,8,22}*1408, {2,22,8,2}*1408, {22,2,8,2}*1408, {2,2,88,2}*1408
   23-fold covers : {2,2,4,46}*1472, {2,46,4,2}*1472, {46,2,4,2}*1472, {2,2,92,2}*1472
   25-fold covers : {2,2,100,2}*1600, {2,2,4,50}*1600, {2,50,4,2}*1600, {50,2,4,2}*1600, {2,2,20,10}*1600a, {2,2,20,10}*1600b, {2,10,20,2}*1600a, {2,10,20,2}*1600b, {10,2,20,2}*1600, {2,10,4,10}*1600, {10,2,4,10}*1600, {10,10,4,2}*1600a, {10,10,4,2}*1600b, {2,2,20,10}*1600c, {2,10,20,2}*1600c, {10,10,4,2}*1600c, {2,2,4,10}*1600, {2,10,4,2}*1600
   26-fold covers : {2,4,4,26}*1664, {2,26,4,4}*1664, {26,2,4,4}*1664, {26,4,4,2}*1664, {2,2,4,52}*1664, {2,2,52,4}*1664, {2,4,52,2}*1664, {2,52,4,2}*1664, {4,2,4,26}*1664, {4,26,4,2}*1664, {4,2,52,2}*1664, {52,2,4,2}*1664, {2,2,8,26}*1664, {2,26,8,2}*1664, {26,2,8,2}*1664, {2,2,104,2}*1664
   27-fold covers : {2,2,108,2}*1728, {2,2,4,54}*1728a, {2,54,4,2}*1728a, {54,2,4,2}*1728, {2,2,12,18}*1728a, {2,18,12,2}*1728a, {18,2,12,2}*1728, {2,2,36,6}*1728a, {2,2,36,6}*1728b, {2,6,36,2}*1728a, {2,6,36,2}*1728b, {6,2,36,2}*1728, {2,2,12,6}*1728a, {2,2,12,6}*1728b, {2,6,12,2}*1728a, {2,6,12,2}*1728b, {6,6,12,2}*1728a, {2,6,4,18}*1728, {2,18,4,6}*1728, {6,2,4,18}*1728a, {6,18,4,2}*1728a, {6,18,4,2}*1728b, {18,2,4,6}*1728a, {18,6,4,2}*1728a, {2,6,12,6}*1728a, {6,6,4,2}*1728a, {6,6,4,2}*1728b, {2,2,12,18}*1728b, {2,18,12,2}*1728b, {18,6,4,2}*1728b, {2,2,12,6}*1728c, {2,6,12,2}*1728c, {6,6,4,2}*1728c, {2,2,4,6}*1728a, {2,2,12,6}*1728e, {2,2,12,6}*1728f, {2,6,4,2}*1728a, {2,6,12,2}*1728e, {2,6,12,2}*1728f, {2,6,12,6}*1728b, {2,6,12,6}*1728c, {2,6,12,6}*1728d, {2,6,12,6}*1728e, {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, {6,6,4,6}*1728a, {6,6,4,6}*1728b, {2,2,12,6}*1728g, {2,6,12,2}*1728g, {6,6,12,2}*1728e, {6,6,4,6}*1728c, {2,6,12,6}*1728f, {2,6,12,6}*1728g, {6,2,12,6}*1728c, {6,6,4,2}*1728h, {6,6,12,2}*1728f, {6,6,12,2}*1728g, {2,2,4,6}*1728b, {2,2,12,6}*1728h, {2,6,4,2}*1728b, {2,6,4,6}*1728a, {2,6,4,6}*1728b, {2,6,12,2}*1728h, {6,2,4,6}*1728, {6,6,4,2}*1728j, {6,6,4,2}*1728k, {2,2,12,6}*1728i, {2,6,12,2}*1728i
   28-fold covers : {4,4,4,14}*1792, {14,4,4,4}*1792, {2,4,4,28}*1792, {2,28,4,4}*1792, {4,4,28,2}*1792, {28,4,4,2}*1792, {2,4,28,4}*1792, {4,28,4,2}*1792, {4,14,4,4}*1792, {28,2,4,4}*1792, {4,2,4,28}*1792, {4,2,28,4}*1792, {2,4,8,14}*1792a, {2,8,4,14}*1792a, {2,14,4,8}*1792a, {2,14,8,4}*1792a, {14,2,4,8}*1792a, {14,2,8,4}*1792a, {14,4,8,2}*1792a, {14,8,4,2}*1792a, {2,2,8,28}*1792a, {2,2,28,8}*1792a, {2,8,28,2}*1792a, {2,28,8,2}*1792a, {2,2,4,56}*1792a, {2,2,56,4}*1792a, {2,4,56,2}*1792a, {2,56,4,2}*1792a, {2,4,8,14}*1792b, {2,8,4,14}*1792b, {2,14,4,8}*1792b, {2,14,8,4}*1792b, {14,2,4,8}*1792b, {14,2,8,4}*1792b, {14,4,8,2}*1792b, {14,8,4,2}*1792b, {2,2,8,28}*1792b, {2,2,28,8}*1792b, {2,8,28,2}*1792b, {2,28,8,2}*1792b, {2,2,4,56}*1792b, {2,2,56,4}*1792b, {2,4,56,2}*1792b, {2,56,4,2}*1792b, {2,4,4,14}*1792, {2,14,4,4}*1792, {14,2,4,4}*1792, {14,4,4,2}*1792, {2,2,4,28}*1792, {2,2,28,4}*1792, {2,4,28,2}*1792, {2,28,4,2}*1792, {4,2,8,14}*1792, {8,2,4,14}*1792, {4,14,8,2}*1792, {8,14,4,2}*1792, {8,2,28,2}*1792, {28,2,8,2}*1792, {4,2,56,2}*1792, {56,2,4,2}*1792, {2,2,16,14}*1792, {2,14,16,2}*1792, {14,2,16,2}*1792, {2,2,112,2}*1792
   29-fold covers : {2,2,4,58}*1856, {2,58,4,2}*1856, {58,2,4,2}*1856, {2,2,116,2}*1856
   30-fold covers : {2,4,4,30}*1920, {2,30,4,4}*1920, {30,2,4,4}*1920, {30,4,4,2}*1920, {2,2,4,60}*1920a, {2,2,60,4}*1920a, {2,4,60,2}*1920a, {2,60,4,2}*1920a, {6,4,4,10}*1920, {6,10,4,4}*1920, {10,4,4,6}*1920, {10,6,4,4}*1920, {2,4,12,10}*1920a, {2,10,4,12}*1920, {2,10,12,4}*1920a, {2,12,4,10}*1920, {10,2,4,12}*1920a, {10,2,12,4}*1920a, {10,4,12,2}*1920, {10,12,4,2}*1920a, {2,4,20,6}*1920, {2,6,4,20}*1920, {2,6,20,4}*1920, {2,20,4,6}*1920, {6,2,4,20}*1920, {6,2,20,4}*1920, {6,4,20,2}*1920, {6,20,4,2}*1920, {2,2,12,20}*1920, {2,2,20,12}*1920, {2,12,20,2}*1920, {2,20,12,2}*1920, {4,2,4,30}*1920a, {4,30,4,2}*1920a, {4,2,60,2}*1920, {60,2,4,2}*1920, {4,6,4,10}*1920a, {4,10,4,6}*1920, {4,2,12,10}*1920, {12,2,4,10}*1920, {4,2,20,6}*1920a, {20,2,4,6}*1920a, {4,10,12,2}*1920, {12,10,4,2}*1920, {4,6,20,2}*1920a, {20,6,4,2}*1920a, {12,2,20,2}*1920, {20,2,12,2}*1920, {2,2,8,30}*1920, {2,30,8,2}*1920, {30,2,8,2}*1920, {2,2,120,2}*1920, {2,6,8,10}*1920, {2,10,8,6}*1920, {6,2,8,10}*1920, {6,10,8,2}*1920, {10,2,8,6}*1920, {10,6,8,2}*1920, {2,2,24,10}*1920, {2,10,24,2}*1920, {10,2,24,2}*1920, {2,2,40,6}*1920, {2,6,40,2}*1920, {6,2,40,2}*1920
   31-fold covers : {2,2,4,62}*1984, {2,62,4,2}*1984, {62,2,4,2}*1984, {2,2,124,2}*1984
Permutation Representation (GAP) : 
s0 := (1,2);;
s1 := (3,4);;
s2 := (6,7);;
s3 := (5,6)(7,8);;
s4 := ( 9,10);;
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*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(10)!(1,2);
s1 := Sym(10)!(3,4);
s2 := Sym(10)!(6,7);
s3 := Sym(10)!(5,6)(7,8);
s4 := Sym(10)!( 9,10);
poly := sub<Sym(10)|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*s2*s3 >;

to this polytope