Chiral Polytope of Type {6,6}

This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{6,6}*1176a with group SmallGroup(1176,225) = C₇² ⋊ D₆ x C₂of order 1176
Rank : 3
Schlafli Type : {6,6}
Rotation Group : SmallGroup(84,7) = (C₇ ⋊ C₆) x C₂ of order 84
Number of vertices, edges, etc : 14, 42, 14
If Aut({6,6}*1176a)=<s₀, s₁, s₂>, then this chiral polytope is ({6,6}*1176a)/N, where
N=<s₀*s₂*s₁*s₀*s₁*s₀*s₂*s₁*s₀*s₂*s₁*s₀*s₂*s₁*s₀*s₁> of order 7
Facet : (Regular) 6-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*sig1*sig1*sig1*sig1, sig1*sig2^-1*sig2^-1*sig1*sig2^-1*sig2^-1, 
sig2*sig2*sig2*sig2*sig2*sig2, sig1*sig2^-1*sig1^-1*sig1^-1*sig1^-1*sig2*sig2*sig1*sig2^-1*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*sig1*sig1*sig1*sig1, sig1*sig2^-1*sig2^-1*sig1*sig2^-1*sig2^-1, sig2*sig2*sig2*sig2*sig2*sig2, sig1*sig2^-1*sig1^-1*sig1^-1*sig1^-1*sig2*sig2*sig1*sig2^-1*sig1 >;