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