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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,2,2,2}*256
if this polytope has a name.
Group : SmallGroup(256,55643)
Rank : 6
Schlafli Type : {4,4,2,2,2}
Number of vertices, edges, etc : 4, 8, 4, 2, 2, 2
Order of s₀s₁s₂s₃s₄s₅ : 4
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,4,2,2,2,2} of size 512
   {4,4,2,2,2,3} of size 768
   {4,4,2,2,2,5} of size 1280
   {4,4,2,2,2,7} of size 1792
Vertex Figure Of :
   {2,4,4,2,2,2} of size 512
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,2,2,2}*128, {4,2,2,2,2}*128
   4-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,4,2,2}*512, {4,4,2,2,4}*512, {4,4,2,4,2}*512, {4,8,2,2,2}*512a, {8,4,2,2,2}*512a, {4,8,2,2,2}*512b, {8,4,2,2,2}*512b, {4,4,2,2,2}*512
   3-fold covers : {4,4,2,2,6}*768, {4,4,2,6,2}*768, {4,4,6,2,2}*768, {4,12,2,2,2}*768a, {12,4,2,2,2}*768a
   5-fold covers : {4,4,2,2,10}*1280, {4,4,2,10,2}*1280, {4,4,10,2,2}*1280, {4,20,2,2,2}*1280, {20,4,2,2,2}*1280
   7-fold covers : {4,4,2,2,14}*1792, {4,4,2,14,2}*1792, {4,4,14,2,2}*1792, {4,28,2,2,2}*1792, {28,4,2,2,2}*1792
Permutation Representation (GAP) :

s0 := (2,3)(4,6);;
s1 := (1,2)(3,5)(4,7)(6,8);;
s2 := (2,4)(3,6);;
s3 := ( 9,10);;
s4 := (11,12);;
s5 := (13,14);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(14)!(2,3)(4,6);
s1 := Sym(14)!(1,2)(3,5)(4,7)(6,8);
s2 := Sym(14)!(2,4)(3,6);
s3 := Sym(14)!( 9,10);
s4 := Sym(14)!(11,12);
s5 := Sym(14)!(13,14);
poly := sub<Sym(14)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope