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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,4,4}*256
if this polytope has a name.
Group : SmallGroup(256,29080)
Rank : 5
Schlafli Type : {4,2,4,4}
Number of vertices, edges, etc : 4, 4, 4, 8, 4
Order of s₀s₁s₂s₃s₄ : 4
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,4,4,2} of size 512
Vertex Figure Of :
   {2,4,2,4,4} of size 512
   {3,4,2,4,4} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,4,4}*128, {4,2,2,4}*128, {4,2,4,2}*128
   4-fold quotients : {2,2,2,4}*64, {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 : {4,4,4,4}*512
   3-fold covers : {4,6,4,4}*768a, {12,2,4,4}*768, {4,2,4,12}*768a, {4,2,12,4}*768a
   5-fold covers : {4,10,4,4}*1280, {20,2,4,4}*1280, {4,2,4,20}*1280, {4,2,20,4}*1280
   7-fold covers : {4,14,4,4}*1792, {28,2,4,4}*1792, {4,2,4,28}*1792, {4,2,28,4}*1792
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 8,10);;
s3 := ( 5, 6)( 7, 9)( 8,11)(10,12);;
s4 := ( 6, 8)( 7,10);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(12)!(2,3);
s1 := Sym(12)!(1,2)(3,4);
s2 := Sym(12)!( 6, 7)( 8,10);
s3 := Sym(12)!( 5, 6)( 7, 9)( 8,11)(10,12);
s4 := Sym(12)!( 6, 8)( 7,10);
poly := sub<Sym(12)|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, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4 >;

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