Chiral Polytope of Type {20,4}

This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{20,4}*2000b with group SmallGroup(2000,919) = (C₅² ⋊ D₄) x D₅of order 2000
Rank : 3
Schlafli Type : {20,4}
Rotation Group : SmallGroup(200,41) = (C₅ ⋊ C₄) x D₅ of order 200
Number of vertices, edges, etc : 50, 100, 10
If Aut({20,4}*2000b)=<s₀, s₁, s₂>, then this chiral polytope is ({20,4}*2000b)/N, where
N=<s₀*s₂*s₁*s₀*s₁*s₂*s₁*s₀*s₂*s₁*s₀*s₂*s₁*s₀*s₁*s₂*s₁*s₀*s₂*s₁> of order 5
Facet : (Regular) 20-gon
Vertex Figure : (Regular) 4-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, sig2*sig2*sig2*sig2, sig1*sig1*sig2^-1*sig1*sig1*sig1*sig2^-1*sig1, 
sig1^-1*sig2*sig1^-1*sig1^-1*sig2*sig1^-1*sig2^-1*sig2^-1*sig1*sig2^-1*sig1*sig2^-1, 
sig2*sig1*sig1*sig1*sig1*sig1*sig1*sig1*sig2*sig1^-1*sig1^-1*sig2*sig2*sig1^-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, sig2*sig2*sig2*sig2, sig1*sig1*sig2^-1*sig1*sig1*sig1*sig2^-1*sig1, sig1^-1*sig2*sig1^-1*sig1^-1*sig2*sig1^-1*sig2^-1*sig2^-1*sig1*sig2^-1*sig1*sig2^-1, sig2*sig1*sig1*sig1*sig1*sig1*sig1*sig1*sig2*sig1^-1*sig1^-1*sig2*sig2*sig1^-1 >;