Chiral Polytope of Type {6,3}

This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{6,3}*1764 with group SmallGroup(1764,146) = (C₃ x C₇²) ⋊ D₆of order 1764
Rank : 3
Schlafli Type : {6,3}
Rotation Group : SmallGroup(126,9) = C₇ ⋊ (S₃ x C₃) of order 126
Number of vertices, edges, etc : 42, 63, 21
If Aut({6,3}*1764)=<s₀, s₁, s₂>, then this chiral polytope is ({6,3}*1764)/N, where
N=<s₀*s₁*s₀*s₁*s₀*s₂*s₁*s₀*s₁*s₀*s₁*s₂*s₁*s₀*s₁*s₀*s₁*s₂*s₁*s₀*s₁*s₀*s₁*s₂*s₁*s₀*s₁*s₂> of order 7
Facet : (Regular) 6-gon
Vertex Figure : (Regular) 3-gon
Finitely Presented Group Representation of the Rotation Group(GAP) :

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

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

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