Chiral Polytope of Type {12,4}

This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{12,4}*1200 with group SmallGroup(1200,961) = C₅² ⋊ D₄ x S₃of order 1200
Rank : 3
Schlafli Type : {12,4}
Rotation Group : SmallGroup(120,36) = (C₅ ⋊ C₄) x S₃ of order 120
Number of vertices, edges, etc : 30, 60, 10
If Aut({12,4}*1200)=<s₀, s₁, s₂>, then this chiral polytope is ({12,4}*1200)/N, where
N=<s₁*s₀*s₂*s₁*s₀*s₁*s₀*s₂*s₁*s₀*s₁*s₀*s₂*s₁*s₀*s₂> of order 5
Facet : (Regular) 12-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^-1*sig2^-1*sig1^-1*sig2*sig1*sig1*sig2^-1*sig1^-1*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^-1*sig2^-1*sig1^-1*sig2*sig1*sig1*sig2^-1*sig1^-1*sig1^-1 >;