Polytope of Type {8,4,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,2,5}*640a
if this polytope has a name.
Group : SmallGroup(640,13813)
Rank : 5
Schlafli Type : {8,4,2,5}
Number of vertices, edges, etc : 8, 16, 4, 5, 5
Order of s₀s₁s₂s₃s₄ : 40
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,4,2,5,2} of size 1280
Vertex Figure Of :
   {2,8,4,2,5} of size 1280
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,4,2,5}*320, {8,2,2,5}*320
   4-fold quotients : {2,4,2,5}*160, {4,2,2,5}*160
   8-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,4,2,5}*1280a, {8,8,2,5}*1280b, {8,8,2,5}*1280c, {16,4,2,5}*1280a, {16,4,2,5}*1280b, {8,4,2,10}*1280a
   3-fold covers : {8,4,2,15}*1920a, {8,12,2,5}*1920a, {24,4,2,5}*1920a
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 6)( 5, 8)( 9,11)(10,12)(13,15);;
s1 := ( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,10)(11,13)(12,14)(15,16);;
s2 := ( 2, 4)( 3, 6)(10,13)(12,15);;
s3 := (18,19)(20,21);;
s4 := (17,18)(19,20);;
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, 
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(21)!( 2, 3)( 4, 6)( 5, 8)( 9,11)(10,12)(13,15);
s1 := Sym(21)!( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,10)(11,13)(12,14)(15,16);
s2 := Sym(21)!( 2, 4)( 3, 6)(10,13)(12,15);
s3 := Sym(21)!(18,19)(20,21);
s4 := Sym(21)!(17,18)(19,20);
poly := sub<Sym(21)|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, 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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope