Chiral Polytope of Type {3,6}
This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{3,6}*588 with group SmallGroup(588,35) = C72 ⋊ D6of order 588
Rank : 3
Schlafli Type : {3,6}
Rotation Group : SmallGroup(42,1) = C7 ⋊ C6 of order 42
Number of vertices, edges, etc : 7, 21, 14
If Aut({3,6}*588)=<s0, s1, s2>, then this chiral polytope is ({3,6}*588)/N, where
N=<s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 7
Facet : (Regular) 3-gon
Vertex Figure : (Regular) 6-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^-1*sig2^-1*sig1^-1*sig2^-1, sig2*sig2*sig2*sig2*sig2*sig2,
sig2*sig1^-1*sig2*sig2*sig1*sig2^-1*sig1*sig2*sig2 ];;
rotpoly := F / rels;;
Finitely Presented Group Representation of the Rotation Group (Magma) :
rotpoly<sig1,sig2> := Group< sig1,sig2 | sig1*sig1*sig1, sig1^-1*sig2^-1*sig1^-1*sig2^-1,
sig2*sig2*sig2*sig2*sig2*sig2, sig2*sig1^-1*sig2*sig2*sig1*sig2^-1*sig1*sig2*sig2 >;