Polytope of Type {2,8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,6}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240973)
Rank : 4
Schlafli Type : {2,8,6}
Number of vertices, edges, etc : 2, 80, 240, 60
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 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 : {2,8,6}*960a, {2,8,6}*960b, {2,4,6}*960
   4-fold quotients : {2,4,6}*480a, {2,4,6}*480b, {2,4,6}*480c
   8-fold quotients : {2,4,6}*240
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 7, 8)( 9,22)(10,21)(11,23)(12,24)(13,15)(14,16)(17,39)(18,40)(19,37)
(20,38)(25,26)(29,34)(30,33)(31,36)(32,35)(41,42);;
s2 := ( 5,13)( 6,14)( 7,16)( 8,15)( 9,42)(10,41)(11,43)(12,44)(17,36)(18,35)
(19,34)(20,33)(21,27)(22,28)(23,25)(24,26)(29,30)(31,32);;
s3 := ( 3, 4)( 5,27)( 6,28)( 7,25)( 8,26)( 9,40)(10,39)(11,37)(12,38)(13,15)
(14,16)(17,21)(18,22)(19,23)(20,24)(29,32)(30,31)(33,36)(34,35)(43,44);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(44)!(1,2);
s1 := Sym(44)!( 7, 8)( 9,22)(10,21)(11,23)(12,24)(13,15)(14,16)(17,39)(18,40)
(19,37)(20,38)(25,26)(29,34)(30,33)(31,36)(32,35)(41,42);
s2 := Sym(44)!( 5,13)( 6,14)( 7,16)( 8,15)( 9,42)(10,41)(11,43)(12,44)(17,36)
(18,35)(19,34)(20,33)(21,27)(22,28)(23,25)(24,26)(29,30)(31,32);
s3 := Sym(44)!( 3, 4)( 5,27)( 6,28)( 7,25)( 8,26)( 9,40)(10,39)(11,37)(12,38)
(13,15)(14,16)(17,21)(18,22)(19,23)(20,24)(29,32)(30,31)(33,36)(34,35)(43,44);
poly := sub<Sym(44)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s1 >;

to this polytope