Chiral Polytope of Type {45,6}

This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{45,6}*1620a with group SmallGroup(1620,131) = C₅ ⋊ ((C₃ x C₉) ⋊ D₆)of order 1620
Rank : 3
Schlafli Type : {45,6}
Rotation Group : SmallGroup(270,15) = C₄₅ ⋊ C₆ of order 270
Number of vertices, edges, etc : 45, 135, 6
If Aut({45,6}*1620a)=<s₀, s₁, s₂>, then this chiral polytope is ({45,6}*1620a)/N, where
N=<s₁*s₀*s₁*s₀*s₁*s₀*s₁*s₀*s₁*s₀*s₁*s₀*s₁*s₀*s₁*s₀*s₁*s₀*s₁*s₀*s₁*s₀*s₂*s₁*s₀*s₁*s₀*s₂*s₁*s₀*s₂*s₁*s₀*s₂> of order 3
Facet : (Regular) 45-gon
Vertex Figure : (Regular) 6-gon
Finitely Presented Group Representation of the Rotation Group(GAP) :

F := FreeGroup("sig1","sig2");;
sig1 := F.1;;  sig2 := F.2;;  
rels := [ sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig1*sig1*sig2^-1*sig1*sig1*sig2^-1, sig2*sig2*sig2*sig2*sig2*sig2, 
sig1^-1*sig2*sig1^-1*sig2^-1*sig2^-1*sig1*sig2^-1*sig2^-1*sig1^-1*sig2, sig1*sig1*sig1*sig2^-1*sig1^-1*sig1^-1*sig1^-1*sig1^-1*sig1^-1*sig2^-1*sig1*sig1*sig1*sig2^-1*sig2^-1*sig1*sig1*sig1*sig1 ];;
rotpoly := F / rels;;

Finitely Presented Group Representation of the Rotation Group (Magma) :

rotpoly<sig1,sig2> := Group< sig1,sig2 | sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig1*sig1*sig2^-1*sig1*sig1*sig2^-1, sig2*sig2*sig2*sig2*sig2*sig2, sig1^-1*sig2*sig1^-1*sig2^-1*sig2^-1*sig1*sig2^-1*sig2^-1*sig1^-1*sig2, sig1*sig1*sig1*sig2^-1*sig1^-1*sig1^-1*sig1^-1*sig1^-1*sig1^-1*sig2^-1*sig1*sig1*sig1*sig2^-1*sig2^-1*sig1*sig1*sig1*sig1 >;