Polytope of Type {8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6}*480a
if this polytope has a name.
Group : SmallGroup(480,948)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 40, 120, 30
Order of s₀s₁s₂ : 5
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {8,6,2} of size 960
Vertex Figure Of :
   {2,8,6} of size 960
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6}*240c
   4-fold quotients : {4,6}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,6}*960a
   3-fold covers : {8,6}*1440b, {24,6}*1440b
   4-fold covers : {8,12}*1920a, {8,6}*1920b, {8,12}*1920d
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope