Chiral Polytope of Type {7,7}

This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{7,7}*896 with group SmallGroup(896,19344) = C₂⁶ ⋊ D₇of order 896
Rank : 3
Schlafli Type : {7,7}
Rotation Group : SmallGroup(56,11) = C₂³ ⋊ C₇ of order 56
Number of vertices, edges, etc : 8, 28, 8
If Aut({7,7}*896)=<s₀, s₁, s₂>, then this chiral polytope is ({7,7}*896)/N, where
N=<s₀*s₁*s₂*s₁*s₀*s₁*s₂*s₁*s₂*s₁*s₀*s₁*s₀*s₁, s₀*s₁*s₀*s₁*s₂*s₁*s₂*s₁*s₂*s₁*s₀*s₁*s₂*s₁, s₀*s₁*s₂*s₁*s₂*s₁*s₂*s₁*s₀*s₁*s₂*s₁*s₀*s₁> of order 8
Facet : (Regular) 7-gon
Vertex Figure : (Regular) 7-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, 
sig1*sig1*sig1*sig2^-1*sig1*sig2^-1*sig2^-1 ];;
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, sig1*sig1*sig1*sig2^-1*sig1*sig2^-1*sig2^-1 >;