Polytope of Type {30,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,6}*540
if this polytope has a name.
Group : SmallGroup(540,54)
Rank : 3
Schlafli Type : {30,6}
Number of vertices, edges, etc : 45, 135, 9
Order of s₀s₁s₂ : 15
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {30,6,2} of size 1080
Vertex Figure Of :
   {2,30,6} of size 1080
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {6,6}*108
Covers (Minimal Covers in Boldface) :
   2-fold covers : {30,6}*1080c
   3-fold covers : {90,6}*1620a, {30,18}*1620a, {30,6}*1620a, {30,6}*1620b, {90,6}*1620b, {30,18}*1620b, {90,6}*1620c, {30,18}*1620c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope