Polytope of Type {8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240560)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 160, 480, 120
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6}*960
   4-fold quotients : {4,6}*480
   8-fold quotients : {4,6}*240a, {4,6}*240b, {4,6}*240c
   16-fold quotients : {4,6}*120
   60-fold quotients : {8,2}*32
   120-fold quotients : {4,2}*16
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 5)( 6,14)( 7,15)( 8,17)( 9,16)(10,18)(11,19)(12,21)(13,20)(22,30)
(23,31)(24,33)(25,32)(26,34)(27,35)(28,37)(29,36);;
s1 := ( 2, 3)( 4, 5)( 6,26)( 7,27)( 8,29)( 9,28)(10,22)(11,23)(12,25)(13,24)
(14,36)(15,37)(16,34)(17,35)(18,32)(19,33)(20,30)(21,31);;
s2 := ( 1, 2)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)(22,26)
(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;

References : None.
to this polytope