Chiral Polytope of Type {4,8}

This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{4,8}*1600b with group SmallGroup(1600,6690) = Q₈ ⋊ (C₅² ⋊ D₄)of order 1600
Rank : 3
Schlafli Type : {4,8}
Rotation Group : SmallGroup(160,85) = C₅ ⋊ ((C₄²) ⋊ C₂) of order 160
Number of vertices, edges, etc : 20, 80, 40
If Aut({4,8}*1600b)=<s₀, s₁, s₂>, then this chiral polytope is ({4,8}*1600b)/N, where
N=<s₁*s₂*s₁*s₀*s₁*s₂*s₁*s₀*s₂*s₁*s₀*s₂*s₁*s₀*s₂*s₁*s₀*s₂*s₁*s₀> of order 5
Facet : (Regular) 4-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*sig1*sig1*sig1, sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig1*sig2^-1*sig2^-1*sig2^-1*sig1*sig2^-1*sig2^-1*sig2^-1, 
sig2*sig2*sig2*sig2*sig2*sig2*sig2*sig2, sig1^-1*sig1^-1*sig2^-1*sig1*sig2*sig1^-1*sig2*sig1^-1*sig2*sig2*sig1*sig2^-1 ];;
rotpoly := F / rels;;

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

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