Polytope of Type {4,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,8,2}*256b
if this polytope has a name.
Group : SmallGroup(256,26531)
Rank : 4
Schlafli Type : {4,8,2}
Number of vertices, edges, etc : 8, 32, 16, 2
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,8,2,2} of size 512
   {4,8,2,3} of size 768
   {4,8,2,5} of size 1280
   {4,8,2,7} of size 1792
Vertex Figure Of :
   {2,4,8,2} of size 512
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,4,2}*128
   4-fold quotients : {4,4,2}*64
   8-fold quotients : {2,4,2}*32, {4,2,2}*32
   16-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,8,2}*512a, {8,8,2}*512b, {8,8,2}*512d, {4,8,4}*512f, {4,8,2}*512b, {4,8,2}*512d, {8,8,2}*512e, {8,8,2}*512g
   3-fold covers : {4,8,6}*768b, {4,24,2}*768b, {12,8,2}*768b
   5-fold covers : {4,8,10}*1280b, {4,40,2}*1280b, {20,8,2}*1280b
   7-fold covers : {4,8,14}*1792b, {4,56,2}*1792b, {28,8,2}*1792b
Permutation Representation (GAP) :

s0 := ( 5, 7)( 6, 8)(13,15)(14,16);;
s1 := ( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15);;
s2 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,15)( 6,16)( 7,13)( 8,14);;
s3 := (17,18);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(18)!( 5, 7)( 6, 8)(13,15)(14,16);
s1 := Sym(18)!( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15);
s2 := Sym(18)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,15)( 6,16)( 7,13)( 8,14);
s3 := Sym(18)!(17,18);
poly := sub<Sym(18)|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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;

to this polytope