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 >;