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Polytope of Type {2,2,2,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,8}*128
if this polytope has a name.
Group : SmallGroup(128,2306)
Rank : 5
Schlafli Type : {2,2,2,8}
Number of vertices, edges, etc : 2, 2, 2, 8, 8
Order of s0s1s2s3s4 : 8
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,2,8,2} of size 256
   {2,2,2,8,4} of size 512
   {2,2,2,8,4} of size 512
   {2,2,2,8,6} of size 768
   {2,2,2,8,3} of size 768
   {2,2,2,8,10} of size 1280
   {2,2,2,8,14} of size 1792
Vertex Figure Of :
   {2,2,2,2,8} of size 256
   {3,2,2,2,8} of size 384
   {4,2,2,2,8} of size 512
   {5,2,2,2,8} of size 640
   {6,2,2,2,8} of size 768
   {7,2,2,2,8} of size 896
   {9,2,2,2,8} of size 1152
   {10,2,2,2,8} of size 1280
   {11,2,2,2,8} of size 1408
   {13,2,2,2,8} of size 1664
   {14,2,2,2,8} of size 1792
   {15,2,2,2,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,4}*64
   4-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,4,8}*256a, {2,4,2,8}*256, {4,2,2,8}*256, {2,2,2,16}*256
   3-fold covers : {2,2,2,24}*384, {2,2,6,8}*384, {2,6,2,8}*384, {6,2,2,8}*384
   4-fold covers : {2,2,4,8}*512a, {2,2,8,8}*512a, {2,2,8,8}*512b, {2,8,2,8}*512, {8,2,2,8}*512, {2,4,4,8}*512b, {2,2,4,16}*512a, {2,2,4,16}*512b, {2,4,2,16}*512, {4,2,2,16}*512, {2,2,2,32}*512
   5-fold covers : {2,2,2,40}*640, {2,2,10,8}*640, {2,10,2,8}*640, {10,2,2,8}*640
   6-fold covers : {2,6,4,8}*768a, {6,2,4,8}*768a, {2,2,12,8}*768a, {2,2,4,24}*768a, {4,2,6,8}*768, {4,6,2,8}*768a, {6,4,2,8}*768a, {2,4,6,8}*768a, {2,12,2,8}*768, {12,2,2,8}*768, {2,4,2,24}*768, {4,2,2,24}*768, {2,2,6,16}*768, {2,6,2,16}*768, {6,2,2,16}*768, {2,2,2,48}*768
   7-fold covers : {2,2,2,56}*896, {2,2,14,8}*896, {2,14,2,8}*896, {14,2,2,8}*896
   9-fold covers : {2,2,18,8}*1152, {2,18,2,8}*1152, {18,2,2,8}*1152, {2,2,2,72}*1152, {2,6,6,8}*1152a, {2,6,6,8}*1152b, {6,2,6,8}*1152, {6,6,2,8}*1152a, {6,6,2,8}*1152b, {6,6,2,8}*1152c, {2,2,6,24}*1152a, {2,6,6,8}*1152c, {2,2,6,24}*1152b, {2,2,6,24}*1152c, {2,6,2,24}*1152, {6,2,2,24}*1152, {2,2,6,8}*1152
   10-fold covers : {2,10,4,8}*1280a, {10,2,4,8}*1280a, {2,2,20,8}*1280a, {2,2,4,40}*1280a, {4,2,10,8}*1280, {4,10,2,8}*1280, {10,4,2,8}*1280, {2,4,10,8}*1280, {2,20,2,8}*1280, {20,2,2,8}*1280, {2,4,2,40}*1280, {4,2,2,40}*1280, {2,2,10,16}*1280, {2,10,2,16}*1280, {10,2,2,16}*1280, {2,2,2,80}*1280
   11-fold covers : {2,2,22,8}*1408, {2,22,2,8}*1408, {22,2,2,8}*1408, {2,2,2,88}*1408
   13-fold covers : {2,2,26,8}*1664, {2,26,2,8}*1664, {26,2,2,8}*1664, {2,2,2,104}*1664
   14-fold covers : {2,14,4,8}*1792a, {14,2,4,8}*1792a, {2,2,28,8}*1792a, {2,2,4,56}*1792a, {4,2,14,8}*1792, {4,14,2,8}*1792, {14,4,2,8}*1792, {2,4,14,8}*1792, {2,28,2,8}*1792, {28,2,2,8}*1792, {2,4,2,56}*1792, {4,2,2,56}*1792, {2,2,14,16}*1792, {2,14,2,16}*1792, {14,2,2,16}*1792, {2,2,2,112}*1792
   15-fold covers : {2,2,30,8}*1920, {2,30,2,8}*1920, {30,2,2,8}*1920, {2,2,2,120}*1920, {2,6,10,8}*1920, {2,10,6,8}*1920, {6,2,10,8}*1920, {6,10,2,8}*1920, {10,2,6,8}*1920, {10,6,2,8}*1920, {2,2,10,24}*1920, {2,10,2,24}*1920, {10,2,2,24}*1920, {2,2,6,40}*1920, {2,6,2,40}*1920, {6,2,2,40}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 8, 9)(10,11)(12,13);;
s4 := ( 7, 8)( 9,10)(11,12)(13,14);;
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, s1*s2*s1*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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(14)!(1,2);
s1 := Sym(14)!(3,4);
s2 := Sym(14)!(5,6);
s3 := Sym(14)!( 8, 9)(10,11)(12,13);
s4 := Sym(14)!( 7, 8)( 9,10)(11,12)(13,14);
poly := sub<Sym(14)|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, 
s1*s2*s1*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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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