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Polytope of Type {4,2,8}

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

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