Polytope of Type {8,2,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,20}*640
if this polytope has a name.
Group : SmallGroup(640,13418)
Rank : 4
Schlafli Type : {8,2,20}
Number of vertices, edges, etc : 8, 8, 20, 20
Order of s₀s₁s₂s₃ : 40
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,2,20,2} of size 1280
Vertex Figure Of :
   {2,8,2,20} of size 1280
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,20}*320, {8,2,10}*320
   4-fold quotients : {8,2,5}*160, {2,2,20}*160, {4,2,10}*160
   5-fold quotients : {8,2,4}*128
   8-fold quotients : {4,2,5}*80, {2,2,10}*80
   10-fold quotients : {4,2,4}*64, {8,2,2}*64
   16-fold quotients : {2,2,5}*40
   20-fold quotients : {2,2,4}*32, {4,2,2}*32
   40-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,40}*1280, {8,4,20}*1280a, {16,2,20}*1280
   3-fold covers : {8,2,60}*1920, {8,6,20}*1920, {24,2,20}*1920
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (10,11)(12,13)(15,18)(16,17)(19,20)(21,22)(23,26)(24,25)(27,28);;
s3 := ( 9,15)(10,12)(11,21)(13,23)(14,17)(16,19)(18,27)(20,24)(22,25)(26,28);;
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(28)!(2,3)(4,5)(6,7);
s1 := Sym(28)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(28)!(10,11)(12,13)(15,18)(16,17)(19,20)(21,22)(23,26)(24,25)(27,28);
s3 := Sym(28)!( 9,15)(10,12)(11,21)(13,23)(14,17)(16,19)(18,27)(20,24)(22,25)
(26,28);
poly := sub<Sym(28)|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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope