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

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

to this polytope