Chiral Polytope of Type {8,8}

This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{8,8}*1296 with group SmallGroup(1296,3509) = C₃⁴ ⋊ (C₈ ⋊ C₂)of order 1296
Rank : 3
Schlafli Type : {8,8}
Rotation Group : SmallGroup(72,39) = C₃² ⋊ C₈ of order 72
Number of vertices, edges, etc : 9, 36, 9
If Aut({8,8}*1296)=<s₀, s₁, s₂>, then this chiral polytope is ({8,8}*1296)/N, where
N=<s₀*s₁*s₀*s₁*s₂*s₁*s₀*s₂*s₁*s₂*s₁*s₀*s₁*s₂, s₀*s₁*s₀*s₂*s₁*s₂*s₁*s₂*s₁*s₀*s₁*s₂*s₁*s₂> of order 9
Facet : (Regular) 8-gon
Vertex Figure : (Regular) 8-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*sig2*sig2*sig2*sig1^-1*sig2*sig2*sig1, 
sig1*sig1*sig2^-1*sig2^-1*sig2^-1*sig1*sig2^-1*sig1, sig1*sig1*sig1*sig1*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*sig2*sig2*sig2*sig1^-1*sig2*sig2*sig1, sig1*sig1*sig2^-1*sig2^-1*sig2^-1*sig1*sig2^-1*sig1, sig1*sig1*sig1*sig1*sig1*sig1*sig1*sig1 >;