Polytope of Type {8,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,2}*64
if this polytope has a name.
Group : SmallGroup(64,250)
Rank : 4
Schlafli Type : {8,2,2}
Number of vertices, edges, etc : 8, 8, 2, 2
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,2,2,2} of size 128
   {8,2,2,3} of size 192
   {8,2,2,4} of size 256
   {8,2,2,5} of size 320
   {8,2,2,6} of size 384
   {8,2,2,7} of size 448
   {8,2,2,8} of size 512
   {8,2,2,9} of size 576
   {8,2,2,10} of size 640
   {8,2,2,11} of size 704
   {8,2,2,12} of size 768
   {8,2,2,13} of size 832
   {8,2,2,14} of size 896
   {8,2,2,15} of size 960
   {8,2,2,17} of size 1088
   {8,2,2,18} of size 1152
   {8,2,2,19} of size 1216
   {8,2,2,20} of size 1280
   {8,2,2,21} of size 1344
   {8,2,2,22} of size 1408
   {8,2,2,23} of size 1472
   {8,2,2,25} of size 1600
   {8,2,2,26} of size 1664
   {8,2,2,27} of size 1728
   {8,2,2,28} of size 1792
   {8,2,2,29} of size 1856
   {8,2,2,30} of size 1920
   {8,2,2,31} of size 1984
Vertex Figure Of :
   {2,8,2,2} of size 128
   {4,8,2,2} of size 256
   {4,8,2,2} of size 256
   {6,8,2,2} of size 384
   {3,8,2,2} of size 384
   {4,8,2,2} of size 512
   {8,8,2,2} of size 512
   {8,8,2,2} of size 512
   {8,8,2,2} of size 512
   {8,8,2,2} of size 512
   {4,8,2,2} of size 512
   {10,8,2,2} of size 640
   {12,8,2,2} of size 768
   {12,8,2,2} of size 768
   {3,8,2,2} of size 768
   {6,8,2,2} of size 768
   {6,8,2,2} of size 768
   {6,8,2,2} of size 768
   {14,8,2,2} of size 896
   {18,8,2,2} of size 1152
   {6,8,2,2} of size 1152
   {9,8,2,2} of size 1152
   {20,8,2,2} of size 1280
   {20,8,2,2} of size 1280
   {5,8,2,2} of size 1280
   {5,8,2,2} of size 1280
   {3,8,2,2} of size 1344
   {3,8,2,2} of size 1344
   {4,8,2,2} of size 1344
   {4,8,2,2} of size 1344
   {6,8,2,2} of size 1344
   {6,8,2,2} of size 1344
   {7,8,2,2} of size 1344
   {7,8,2,2} of size 1344
   {8,8,2,2} of size 1344
   {8,8,2,2} of size 1344
   {22,8,2,2} of size 1408
   {26,8,2,2} of size 1664
   {28,8,2,2} of size 1792
   {28,8,2,2} of size 1792
   {30,8,2,2} of size 1920
   {15,8,2,2} of size 1920
   {5,8,2,2} of size 1920
   {6,8,2,2} of size 1920
   {6,8,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,2}*32
   4-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,4,2}*128a, {8,2,4}*128, {16,2,2}*128
   3-fold covers : {24,2,2}*192, {8,2,6}*192, {8,6,2}*192
   4-fold covers : {8,4,2}*256a, {8,8,2}*256b, {8,8,2}*256c, {8,2,8}*256, {8,4,4}*256a, {16,4,2}*256a, {16,4,2}*256b, {16,2,4}*256, {32,2,2}*256
   5-fold covers : {40,2,2}*320, {8,2,10}*320, {8,10,2}*320
   6-fold covers : {24,4,2}*384a, {8,12,2}*384a, {24,2,4}*384, {8,2,12}*384, {8,4,6}*384a, {8,6,4}*384a, {48,2,2}*384, {16,2,6}*384, {16,6,2}*384
   7-fold covers : {56,2,2}*448, {8,2,14}*448, {8,14,2}*448
   8-fold covers : {8,8,2}*512a, {8,4,8}*512b, {8,8,4}*512a, {8,4,4}*512a, {8,8,4}*512c, {8,8,4}*512e, {8,8,4}*512g, {8,4,4}*512b, {8,4,8}*512c, {8,4,2}*512a, {8,8,2}*512d, {16,4,2}*512a, {16,4,2}*512b, {8,16,2}*512a, {8,16,2}*512b, {8,16,2}*512d, {16,8,2}*512c, {16,8,2}*512d, {8,16,2}*512f, {16,8,2}*512e, {16,8,2}*512f, {16,4,4}*512a, {16,4,4}*512b, {32,4,2}*512a, {32,4,2}*512b, {64,2,2}*512
   9-fold covers : {72,2,2}*576, {8,2,18}*576, {8,18,2}*576, {24,2,6}*576, {24,6,2}*576a, {24,6,2}*576b, {8,6,6}*576a, {8,6,6}*576b, {8,6,6}*576c, {24,6,2}*576c, {8,6,2}*576
   10-fold covers : {40,4,2}*640a, {8,20,2}*640a, {40,2,4}*640, {8,2,20}*640, {8,4,10}*640a, {8,10,4}*640, {80,2,2}*640, {16,2,10}*640, {16,10,2}*640
   11-fold covers : {88,2,2}*704, {8,2,22}*704, {8,22,2}*704
   12-fold covers : {8,4,6}*768a, {8,12,2}*768a, {24,4,2}*768a, {8,8,6}*768b, {8,8,6}*768c, {8,24,2}*768a, {8,24,2}*768c, {24,8,2}*768b, {24,8,2}*768c, {8,6,8}*768, {8,2,24}*768, {24,2,8}*768, {8,4,12}*768a, {8,12,4}*768a, {24,4,4}*768a, {16,4,6}*768a, {16,12,2}*768a, {48,4,2}*768a, {16,4,6}*768b, {16,12,2}*768b, {48,4,2}*768b, {16,6,4}*768a, {16,2,12}*768, {48,2,4}*768, {32,2,6}*768, {32,6,2}*768, {96,2,2}*768, {24,4,2}*768c, {8,4,6}*768c, {8,6,4}*768a, {8,6,6}*768, {8,6,2}*768g, {24,6,2}*768a
   13-fold covers : {104,2,2}*832, {8,2,26}*832, {8,26,2}*832
   14-fold covers : {56,4,2}*896a, {8,28,2}*896a, {56,2,4}*896, {8,2,28}*896, {8,4,14}*896a, {8,14,4}*896, {112,2,2}*896, {16,2,14}*896, {16,14,2}*896
   15-fold covers : {24,2,10}*960, {24,10,2}*960, {40,2,6}*960, {40,6,2}*960, {8,6,10}*960, {8,10,6}*960, {120,2,2}*960, {8,2,30}*960, {8,30,2}*960
   17-fold covers : {8,2,34}*1088, {8,34,2}*1088, {136,2,2}*1088
   18-fold covers : {8,4,18}*1152a, {8,36,2}*1152a, {72,4,2}*1152a, {8,12,6}*1152a, {8,12,6}*1152b, {8,12,6}*1152c, {24,4,6}*1152a, {24,12,2}*1152a, {24,12,2}*1152b, {24,12,2}*1152c, {8,4,6}*1152a, {8,4,2}*1152a, {24,4,2}*1152a, {8,12,2}*1152a, {8,18,4}*1152a, {8,2,36}*1152, {72,2,4}*1152, {8,6,12}*1152a, {8,6,12}*1152b, {8,6,12}*1152c, {24,6,4}*1152a, {24,6,4}*1152b, {24,6,4}*1152c, {24,2,12}*1152, {8,4,4}*1152, {8,6,4}*1152a, {8,6,4}*1152b, {16,2,18}*1152, {16,18,2}*1152, {144,2,2}*1152, {16,6,6}*1152a, {16,6,6}*1152b, {16,6,6}*1152c, {48,6,2}*1152a, {48,2,6}*1152, {48,6,2}*1152b, {48,6,2}*1152c, {16,6,2}*1152
   19-fold covers : {8,2,38}*1216, {8,38,2}*1216, {152,2,2}*1216
   20-fold covers : {8,4,10}*1280a, {8,20,2}*1280a, {40,4,2}*1280a, {8,8,10}*1280b, {8,8,10}*1280c, {8,40,2}*1280a, {8,40,2}*1280c, {40,8,2}*1280b, {40,8,2}*1280c, {8,10,8}*1280, {8,2,40}*1280, {40,2,8}*1280, {8,4,20}*1280a, {8,20,4}*1280a, {40,4,4}*1280a, {16,4,10}*1280a, {16,20,2}*1280a, {80,4,2}*1280a, {16,4,10}*1280b, {16,20,2}*1280b, {80,4,2}*1280b, {16,10,4}*1280, {16,2,20}*1280, {80,2,4}*1280, {32,2,10}*1280, {32,10,2}*1280, {160,2,2}*1280
   21-fold covers : {24,2,14}*1344, {24,14,2}*1344, {56,2,6}*1344, {56,6,2}*1344, {8,6,14}*1344, {8,14,6}*1344, {168,2,2}*1344, {8,2,42}*1344, {8,42,2}*1344
   22-fold covers : {8,4,22}*1408a, {8,44,2}*1408a, {88,4,2}*1408a, {8,22,4}*1408, {8,2,44}*1408, {88,2,4}*1408, {16,2,22}*1408, {16,22,2}*1408, {176,2,2}*1408
   23-fold covers : {8,2,46}*1472, {8,46,2}*1472, {184,2,2}*1472
   25-fold covers : {200,2,2}*1600, {8,2,50}*1600, {8,50,2}*1600, {40,2,10}*1600, {40,10,2}*1600a, {40,10,2}*1600b, {8,10,10}*1600a, {8,10,10}*1600b, {8,10,10}*1600c, {40,10,2}*1600c, {8,10,2}*1600
   26-fold covers : {8,4,26}*1664a, {8,52,2}*1664a, {104,4,2}*1664a, {8,26,4}*1664, {8,2,52}*1664, {104,2,4}*1664, {16,2,26}*1664, {16,26,2}*1664, {208,2,2}*1664
   27-fold covers : {216,2,2}*1728, {8,2,54}*1728, {8,54,2}*1728, {72,2,6}*1728, {72,6,2}*1728a, {72,6,2}*1728b, {24,2,18}*1728, {24,18,2}*1728a, {24,6,6}*1728a, {24,6,2}*1728a, {24,6,2}*1728b, {8,6,18}*1728a, {8,18,6}*1728a, {8,18,6}*1728b, {8,6,6}*1728a, {8,6,6}*1728b, {8,6,18}*1728b, {24,18,2}*1728b, {8,6,6}*1728c, {24,6,2}*1728c, {8,6,2}*1728a, {24,6,2}*1728d, {24,6,2}*1728e, {24,6,6}*1728b, {24,6,6}*1728c, {24,6,6}*1728d, {24,6,6}*1728e, {24,6,2}*1728f, {8,6,6}*1728e, {24,6,6}*1728f, {24,6,6}*1728g, {8,6,6}*1728f, {8,6,6}*1728g, {8,6,2}*1728b, {24,6,2}*1728g, {24,6,2}*1728h
   28-fold covers : {8,4,14}*1792a, {8,28,2}*1792a, {56,4,2}*1792a, {8,8,14}*1792b, {8,8,14}*1792c, {8,56,2}*1792a, {8,56,2}*1792c, {56,8,2}*1792b, {56,8,2}*1792c, {8,14,8}*1792, {8,2,56}*1792, {56,2,8}*1792, {8,4,28}*1792a, {8,28,4}*1792a, {56,4,4}*1792a, {16,4,14}*1792a, {16,28,2}*1792a, {112,4,2}*1792a, {16,4,14}*1792b, {16,28,2}*1792b, {112,4,2}*1792b, {16,14,4}*1792, {16,2,28}*1792, {112,2,4}*1792, {32,2,14}*1792, {32,14,2}*1792, {224,2,2}*1792
   29-fold covers : {8,2,58}*1856, {8,58,2}*1856, {232,2,2}*1856
   30-fold covers : {8,4,30}*1920a, {8,60,2}*1920a, {120,4,2}*1920a, {8,12,10}*1920a, {8,20,6}*1920a, {24,4,10}*1920a, {40,4,6}*1920a, {40,12,2}*1920a, {24,20,2}*1920a, {8,30,4}*1920a, {8,2,60}*1920, {120,2,4}*1920, {8,10,12}*1920, {8,6,20}*1920, {24,10,4}*1920, {40,6,4}*1920a, {40,2,12}*1920, {24,2,20}*1920, {16,2,30}*1920, {16,30,2}*1920, {240,2,2}*1920, {16,6,10}*1920, {16,10,6}*1920, {48,2,10}*1920, {48,10,2}*1920, {80,2,6}*1920, {80,6,2}*1920
   31-fold covers : {8,2,62}*1984, {8,62,2}*1984, {248,2,2}*1984
Permutation Representation (GAP) : 
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := ( 9,10);;
s3 := (11,12);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(12)!(2,3)(4,5)(6,7);
s1 := Sym(12)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(12)!( 9,10);
s3 := Sym(12)!(11,12);
poly := sub<Sym(12)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope