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Polytope of Type {8,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,4}*128
if this polytope has a name.
Group : SmallGroup(128,2011)
Rank : 4
Schlafli Type : {8,2,4}
Number of vertices, edges, etc : 8, 8, 4, 4
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,2,4,2} of size 256
   {8,2,4,3} of size 384
   {8,2,4,6} of size 768
   {8,2,4,3} of size 768
   {8,2,4,6} of size 768
   {8,2,4,6} of size 768
   {8,2,4,4} of size 1152
   {8,2,4,6} of size 1152
   {8,2,4,9} of size 1152
   {8,2,4,10} of size 1280
   {8,2,4,14} of size 1792
   {8,2,4,15} of size 1920
   {8,2,4,5} of size 1920
   {8,2,4,6} of size 1920
Vertex Figure Of :
   {2,8,2,4} of size 256
   {6,8,2,4} of size 768
   {3,8,2,4} of size 768
   {10,8,2,4} of size 1280
   {14,8,2,4} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,4}*64, {8,2,2}*64
   4-fold quotients : {2,2,4}*32, {4,2,2}*32
   8-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,8}*256, {8,4,4}*256a, {16,2,4}*256
   3-fold covers : {24,2,4}*384, {8,2,12}*384, {8,6,4}*384a
   4-fold covers : {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, {16,4,4}*512a, {16,4,4}*512b
   5-fold covers : {40,2,4}*640, {8,2,20}*640, {8,10,4}*640
   6-fold covers : {8,6,8}*768, {8,2,24}*768, {24,2,8}*768, {8,4,12}*768a, {8,12,4}*768a, {24,4,4}*768a, {16,6,4}*768a, {16,2,12}*768, {48,2,4}*768
   7-fold covers : {56,2,4}*896, {8,2,28}*896, {8,14,4}*896
   9-fold covers : {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, {8,6,4}*1152a, {8,6,4}*1152b
   10-fold covers : {8,10,8}*1280, {8,2,40}*1280, {40,2,8}*1280, {8,4,20}*1280a, {8,20,4}*1280a, {40,4,4}*1280a, {16,10,4}*1280, {16,2,20}*1280, {80,2,4}*1280
   11-fold covers : {8,22,4}*1408, {8,2,44}*1408, {88,2,4}*1408
   13-fold covers : {8,26,4}*1664, {8,2,52}*1664, {104,2,4}*1664
   14-fold covers : {8,14,8}*1792, {8,2,56}*1792, {56,2,8}*1792, {8,4,28}*1792a, {8,28,4}*1792a, {56,4,4}*1792a, {16,14,4}*1792, {16,2,28}*1792, {112,2,4}*1792
   15-fold covers : {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
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (10,11);;
s3 := ( 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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*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)!(10,11);
s3 := Sym(12)!( 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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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