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

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

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := ( 9,10);;
s3 := (12,13);;
s4 := (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*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, 
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)!( 9,10);
s3 := Sym(14)!(12,13);
s4 := Sym(14)!(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*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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

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