Chiral Polytope of Type {9,12}
This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{9,12}*1296c with group SmallGroup(1296,1789) = C32 ⋊ (((C22 ⋊ C9) ⋊ C2) x C2)of order 1296
Rank : 3
Schlafli Type : {9,12}
Rotation Group : SmallGroup(216,90) = ((C22 ⋊ C9) ⋊ C2) ⋊ C3 of order 216
Number of vertices, edges, etc : 18, 108, 24
If Aut({9,12}*1296c)=<s0, s1, s2>, then this chiral polytope is ({9,12}*1296c)/N, where
N=<s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1> of order 3
Facet : (Regular) 9-gon
Vertex Figure : (Regular) 12-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*sig2^-1*sig1*sig1*sig2^-1, sig1*sig1*sig1*sig1*sig1*sig1*sig1*sig1*sig1,
sig1^-1*sig2*sig1^-1*sig2^-1*sig2^-1*sig1*sig2^-1*sig2^-1*sig1^-1*sig2, sig1^-1*sig2*sig2*sig2*sig2*sig2*sig1*sig2^-1*sig2^-1*sig2^-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, sig1*sig1*sig2^-1*sig1*sig1*sig2^-1,
sig1*sig1*sig1*sig1*sig1*sig1*sig1*sig1*sig1, sig1^-1*sig2*sig1^-1*sig2^-1*sig2^-1*sig1*sig2^-1*sig2^-1*sig1^-1*sig2,
sig1^-1*sig2*sig2*sig2*sig2*sig2*sig1*sig2^-1*sig2^-1*sig2^-1*sig1^-1 >;