Polytope of Type {8,2,4,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,4,10}*1280
if this polytope has a name.
Group : SmallGroup(1280,1044755)
Rank : 5
Schlafli Type : {8,2,4,10}
Number of vertices, edges, etc : 8, 8, 4, 20, 10
Order of s₀s₁s₂s₃s₄ : 40
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,4,10}*640, {8,2,2,10}*640
   4-fold quotients : {8,2,2,5}*320, {2,2,4,10}*320, {4,2,2,10}*320
   5-fold quotients : {8,2,4,2}*256
   8-fold quotients : {4,2,2,5}*160, {2,2,2,10}*160
   10-fold quotients : {4,2,4,2}*128, {8,2,2,2}*128
   16-fold quotients : {2,2,2,5}*80
   20-fold quotients : {2,2,4,2}*64, {4,2,2,2}*64
   40-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (10,13)(14,19)(15,20)(21,25)(22,26);;
s3 := ( 9,10)(11,15)(12,14)(13,18)(16,22)(17,21)(19,24)(20,23)(25,28)(26,27);;
s4 := ( 9,11)(10,14)(12,16)(13,19)(15,21)(18,23)(20,25)(24,27);;
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*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
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(28)!(2,3)(4,5)(6,7);
s1 := Sym(28)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(28)!(10,13)(14,19)(15,20)(21,25)(22,26);
s3 := Sym(28)!( 9,10)(11,15)(12,14)(13,18)(16,22)(17,21)(19,24)(20,23)(25,28)
(26,27);
s4 := Sym(28)!( 9,11)(10,14)(12,16)(13,19)(15,21)(18,23)(20,25)(24,27);
poly := sub<Sym(28)|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*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, 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