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

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

s0 := (2,3);;
s1 := (1,2)(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*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, s0*s1*s0*s1*s0*s1*s0*s1, 
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)!(2,3);
s1 := Sym(14)!(1,2)(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*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, 
s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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