Polytope of Type {6,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,20}*360
if this polytope has a name.
Group : SmallGroup(360,134)
Rank : 3
Schlafli Type : {6,20}
Number of vertices, edges, etc : 9, 90, 30
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,20,2} of size 720
   {6,20,4} of size 1440
Vertex Figure Of :
   {2,6,20} of size 720
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {6,4}*72
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,20}*720
   3-fold covers : {6,20}*1080, {6,60}*1080a, {6,60}*1080b, {6,60}*1080c
   4-fold covers : {6,40}*1440, {12,20}*1440
   5-fold covers : {6,100}*1800
Permutation Representation (GAP) :

s0 := ( 6,11)( 7,12)( 8,13)( 9,14)(10,15)(16,31)(17,32)(18,33)(19,34)(20,35)
(21,41)(22,42)(23,43)(24,44)(25,45)(26,36)(27,37)(28,38)(29,39)(30,40);;
s1 := ( 1, 6)( 2,10)( 3, 9)( 4, 8)( 5, 7)(12,15)(13,14)(16,21)(17,25)(18,24)
(19,23)(20,22)(27,30)(28,29)(31,36)(32,40)(33,39)(34,38)(35,37)(42,45)
(43,44);;
s2 := ( 1, 2)( 3, 5)( 6,17)( 7,16)( 8,20)( 9,19)(10,18)(11,32)(12,31)(13,35)
(14,34)(15,33)(21,22)(23,25)(26,37)(27,36)(28,40)(29,39)(30,38)(41,42)
(43,45);;
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*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(45)!( 6,11)( 7,12)( 8,13)( 9,14)(10,15)(16,31)(17,32)(18,33)(19,34)
(20,35)(21,41)(22,42)(23,43)(24,44)(25,45)(26,36)(27,37)(28,38)(29,39)(30,40);
s1 := Sym(45)!( 1, 6)( 2,10)( 3, 9)( 4, 8)( 5, 7)(12,15)(13,14)(16,21)(17,25)
(18,24)(19,23)(20,22)(27,30)(28,29)(31,36)(32,40)(33,39)(34,38)(35,37)(42,45)
(43,44);
s2 := Sym(45)!( 1, 2)( 3, 5)( 6,17)( 7,16)( 8,20)( 9,19)(10,18)(11,32)(12,31)
(13,35)(14,34)(15,33)(21,22)(23,25)(26,37)(27,36)(28,40)(29,39)(30,38)(41,42)
(43,45);
poly := sub<Sym(45)|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*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope