Chiral Polytope of Type {7,14}

This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{7,14}*1792d with group SmallGroup(1792,1083553) = (C₂⁶ ⋊ D₇) x C₂of order 1792
Rank : 3
Schlafli Type : {7,14}
Rotation Group : SmallGroup(112,41) = (C₂³ ⋊ C₇) x C₂ of order 112
Number of vertices, edges, etc : 8, 56, 16
If Aut({7,14}*1792d)=<s₀, s₁, s₂>, then this chiral polytope is ({7,14}*1792d)/N, where
N=<s₁*s₂*s₁*s₀*s₁*s₂*s₁*s₀*s₁*s₀*s₁*s₂*s₁*s₂, s₀*s₁*s₂*s₁*s₂*s₁*s₂*s₁*s₀*s₁*s₀*s₁*s₂*s₁, s₀*s₁*s₂*s₁*s₀*s₁*s₂*s₁*s₂*s₁*s₂*s₁*s₀*s₁> of order 8
Facet : (Regular) 7-gon
Vertex Figure : (Regular) 14-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*sig2^-1*sig1*sig2^-1*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*sig2^-1*sig1*sig2^-1*sig2^-1*sig2^-1 >;