Polytope of Type {8,2,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,8}*256
if this polytope has a name.
Group : SmallGroup(256,12955)
Rank : 4
Schlafli Type : {8,2,8}
Number of vertices, edges, etc : 8, 8, 8, 8
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,2,8,2} of size 512
Vertex Figure Of :
   {2,8,2,8} of size 512
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,8}*128, {8,2,4}*128
   4-fold quotients : {4,2,4}*64, {2,2,8}*64, {8,2,2}*64
   8-fold quotients : {2,2,4}*32, {4,2,2}*32
   16-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,4,8}*512b
   3-fold covers : {8,6,8}*768, {8,2,24}*768, {24,2,8}*768
   5-fold covers : {8,10,8}*1280, {8,2,40}*1280, {40,2,8}*1280
   7-fold covers : {8,14,8}*1792, {8,2,56}*1792, {56,2,8}*1792
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (10,11)(12,13)(14,15);;
s3 := ( 9,10)(11,12)(13,14)(15,16);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(16)!(2,3)(4,5)(6,7);
s1 := Sym(16)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(16)!(10,11)(12,13)(14,15);
s3 := Sym(16)!( 9,10)(11,12)(13,14)(15,16);
poly := sub<Sym(16)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

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

to this polytope