Chiral Polytope of Type {8,3,3}
This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{8,3,3}*768b with group SmallGroup(768,1086052) = ((Q8 x C2) ⋊ C2) ⋊ S4of order 768
Rank : 4
Schlafli Type : {8,3,3}
Rotation Group : SmallGroup(192,1494) = Q8 ⋊ S4 of order 192
Number of vertices, edges, etc : 16, 32, 12, 4
If Aut({8,3,3}*768b)=<s0, s1, s2, s3>, then this chiral polytope is ({8,3,3}*768b)/N, where
N=<s0*s1*s0*s1*s2*s1*s3*s2*s1*s0*s1*s0*s2*s1*s3*s2> of order 2
Facet : Regular {8,3}*96
Vertex Figure : Regular {3,3}*24
Finitely Presented Group Representation of the Rotation Group(GAP) :
F := FreeGroup("sig1","sig2","sig3");;
sig1 := F.1;; sig2 := F.2;; sig3 := F.3;;
rels := [ sig2*sig2*sig2, sig3*sig3*sig3, sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig2^-1*sig3^-1*sig2^-1*sig3^-1,
sig1*sig2^-1*sig3*sig1^-1*sig3^-1, sig2^-1*sig1*sig3^-1*sig1^-1*sig2*sig3^-1*sig1^-1*sig1^-1,
sig1*sig1*sig1*sig1*sig1*sig1*sig1*sig1, sig1*sig1*sig2^-1*sig1*sig1*sig1*sig2^-1*sig1 ];;
rotpoly := F / rels;;
Finitely Presented Group Representation of the Rotation Group (Magma) :
rotpoly<sig1,sig2,sig3> := Group< sig1,sig2,sig3 | sig2*sig2*sig2, sig3*sig3*sig3,
sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig2^-1*sig3^-1*sig2^-1*sig3^-1, sig1*sig2^-1*sig3*sig1^-1*sig3^-1,
sig2^-1*sig1*sig3^-1*sig1^-1*sig2*sig3^-1*sig1^-1*sig1^-1, sig1*sig1*sig1*sig1*sig1*sig1*sig1*sig1,
sig1*sig1*sig2^-1*sig1*sig1*sig1*sig2^-1*sig1 >;