Chiral Polytope of Type {6,6,9}
This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{6,6,9}*1944a with group SmallGroup(1944,949) = (C33 ⋊ (D9 x C2)) x C2of order 1944
Rank : 4
Schlafli Type : {6,6,9}
Rotation Group : SmallGroup(324,77) = ((C33 ⋊ C3) ⋊ C2) x C2 of order 324
Number of vertices, edges, etc : 6, 18, 27, 9
If Aut({6,6,9}*1944a)=<s0, s1, s2, s3>, then this chiral polytope is ({6,6,9}*1944a)/N, where
N=<s0*s1*s2*s1*s0*s3*s2*s1*s3*s2*s1*s3> of order 3
Facet : Regular {6,6}*72c
Vertex Figure : Chiral Quotient of {6,9}*324a
Finitely Presented Group Representation of the Rotation Group(GAP) :
F := FreeGroup("sig1","sig2","sig3");;
sig1 := F.1;; sig2 := F.2;; sig3 := F.3;;
rels := [ sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig2^-1*sig3^-1*sig2^-1*sig3^-1, sig1^-1*sig2^-1*sig2^-1*sig2^-1*sig1^-1*sig2,
sig1^-1*sig3*sig1*sig2*sig3*sig2^-1, sig2*sig2*sig2*sig2*sig2*sig2,
sig1*sig1*sig1*sig1*sig1*sig1, sig2*sig3^-1*sig3^-1*sig2*sig3^-1*sig3^-1,
sig2*sig2*sig2*sig3*sig2^-1*sig3^-1*sig3^-1 ];;
rotpoly := F / rels;;
Finitely Presented Group Representation of the Rotation Group (Magma) :
rotpoly<sig1,sig2,sig3> := Group< sig1,sig2,sig3 | sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig2^-1*sig3^-1*sig2^-1*sig3^-1,
sig1^-1*sig2^-1*sig2^-1*sig2^-1*sig1^-1*sig2, sig1^-1*sig3*sig1*sig2*sig3*sig2^-1,
sig2*sig2*sig2*sig2*sig2*sig2, sig1*sig1*sig1*sig1*sig1*sig1,
sig2*sig3^-1*sig3^-1*sig2*sig3^-1*sig3^-1, sig2*sig2*sig2*sig3*sig2^-1*sig3^-1*sig3^-1 >;