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Polytope of Type {2,2,8}

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

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