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Polytope of Type {8,2,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,4,2}*256
if this polytope has a name.
Group : SmallGroup(256,54027)
Rank : 5
Schlafli Type : {8,2,4,2}
Number of vertices, edges, etc : 8, 8, 4, 4, 2
Order of s0s1s2s3s4 : 8
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,2,4,2,2} of size 512
   {8,2,4,2,3} of size 768
   {8,2,4,2,5} of size 1280
   {8,2,4,2,7} of size 1792
Vertex Figure Of :
   {2,8,2,4,2} of size 512
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,4,2}*128, {8,2,2,2}*128
   4-fold quotients : {2,2,4,2}*64, {4,2,2,2}*64
   8-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,8,2}*512, {8,4,4,2}*512b, {16,2,4,2}*512
   3-fold covers : {8,2,4,6}*768a, {8,6,4,2}*768a, {8,2,12,2}*768, {24,2,4,2}*768
   5-fold covers : {8,2,4,10}*1280, {8,10,4,2}*1280, {8,2,20,2}*1280, {40,2,4,2}*1280
   7-fold covers : {8,2,4,14}*1792, {8,14,4,2}*1792, {8,2,28,2}*1792, {56,2,4,2}*1792
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);;
s4 := (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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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(14)!(2,3)(4,5)(6,7);
s1 := Sym(14)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(14)!(10,11);
s3 := Sym(14)!( 9,10)(11,12);
s4 := Sym(14)!(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*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
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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