Chiral Polytope of Type {6,27}
This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{6,27}*972a with group SmallGroup(972,107) = (C27 x C3) ⋊ D6of order 972
Rank : 3
Schlafli Type : {6,27}
Rotation Group : SmallGroup(162,9) = (C27 ⋊ C3) ⋊ C2 of order 162
Number of vertices, edges, etc : 6, 81, 27
If Aut({6,27}*972a)=<s0, s1, s2>, then this chiral polytope is ({6,27}*972a)/N, where
N=<s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 3
Facet : (Regular) 6-gon
Vertex Figure : (Regular) 27-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, sig1*sig1*sig1*sig1*sig1*sig1, sig1*sig2^-1*sig2^-1*sig1*sig2^-1*sig2^-1,
sig1*sig2^-1*sig1^-1*sig1^-1*sig2^-1*sig1*sig2^-1*sig1*sig1*sig2^-1, sig2*sig2*sig2*sig1^-1*sig2^-1*sig1*sig2*sig2*sig2*sig2*sig1^-1*sig1^-1*sig2 ];;
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, sig1*sig1*sig1*sig1*sig1*sig1,
sig1*sig2^-1*sig2^-1*sig1*sig2^-1*sig2^-1, sig1*sig2^-1*sig1^-1*sig1^-1*sig2^-1*sig1*sig2^-1*sig1*sig1*sig2^-1,
sig2*sig2*sig2*sig1^-1*sig2^-1*sig1*sig2*sig2*sig2*sig2*sig1^-1*sig1^-1*sig2 >;