Polytope of Type {5,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,6}*480
if this polytope has a name.
Group : SmallGroup(480,948)
Rank : 3
Schlafli Type : {5,6}
Number of vertices, edges, etc : 40, 120, 48
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {5,6,2} of size 960
   {5,6,4} of size 1920
Vertex Figure Of :
   {2,5,6} of size 960
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,6}*240a
   4-fold quotients : {5,6}*120a
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,6}*960a
   3-fold covers : {15,6}*1440a, {15,6}*1440b
   4-fold covers : {10,12}*1920b, {20,6}*1920c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope