Chiral Polytope of Type {18,18}
This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{18,18}*1944b with group SmallGroup(1944,940) = (C3 x C9) ⋊ (D9 x C2) x C2of order 1944
Rank : 3
Schlafli Type : {18,18}
Rotation Group : SmallGroup(324,64) = ((C9 ⋊ C9) ⋊ C2) x C2 of order 324
Number of vertices, edges, etc : 18, 162, 18
If Aut({18,18}*1944b)=<s0, s1, s2>, then this chiral polytope is ({18,18}*1944b)/N, where
N=<s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2> of order 3
Facet : (Regular) 18-gon
Vertex Figure : (Regular) 18-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*sig2^-1*sig1^-1*sig2*sig1^-1*sig2*sig2*sig1*sig1*sig1,
sig1^-1*sig2*sig1*sig1*sig2*sig2*sig2*sig1*sig2^-1*sig2^-1, sig2^-1*sig2^-1*sig2^-1*sig2^-1*sig1*sig2^-1*sig1*sig2^-1*sig2^-1*sig2^-1*sig1*sig1*sig1*sig1*sig1*sig1*sig1*sig1 ];;
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*sig2^-1*sig1^-1*sig2*sig1^-1*sig2*sig2*sig1*sig1*sig1,
sig1^-1*sig2*sig1*sig1*sig2*sig2*sig2*sig1*sig2^-1*sig2^-1, sig2^-1*sig2^-1*sig2^-1*sig2^-1*sig1*sig2^-1*sig1*sig2^-1*sig2^-1*sig2^-1*sig1*sig1*sig1*sig1*sig1*sig1*sig1*sig1 >;