Polytope of Type {8,2,2,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,2,10}*640
if this polytope has a name.
Group : SmallGroup(640,21152)
Rank : 5
Schlafli Type : {8,2,2,10}
Number of vertices, edges, etc : 8, 8, 2, 10, 10
Order of s₀s₁s₂s₃s₄ : 40
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,2,2,10,2} of size 1280
Vertex Figure Of :
   {2,8,2,2,10} of size 1280
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,2,2,5}*320, {4,2,2,10}*320
   4-fold quotients : {4,2,2,5}*160, {2,2,2,10}*160
   5-fold quotients : {8,2,2,2}*128
   8-fold quotients : {2,2,2,5}*80
   10-fold quotients : {4,2,2,2}*64
   20-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,4,2,10}*1280a, {8,2,4,10}*1280, {8,2,2,20}*1280, {16,2,2,10}*1280
   3-fold covers : {8,2,2,30}*1920, {8,2,6,10}*1920, {8,6,2,10}*1920, {24,2,2,10}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope