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

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

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