, Volume 34, Issue 2, pp 181-229
Date: 27 May 2005

Chiral Polyhedra in Ordinary Space, II

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Abstract

A chiral polyhedron has a geometric symmetry group with two orbits on the flags, such that adjacent flags are in distinct orbits. Part I of the paper described the discrete chiral polyhedra in ordinary euclidean space E3 with finite skew faces and finite skew vertex-figures; they occur in infinite families and are of types {4,6}, {6,4} and {6,6}. Part II completes the enumeration of all discrete chiral polyhedra in E3. There exist several families of chiral polyhedra of types {∞,3} and {∞,4} with infinite, helical faces. In particular, there are no discrete chiral polyhedra with finite faces in addition to those described in Part I.