Chiral polyhedra in ordinary space, II

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 3-space 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 3-space. There exist several families of chiral polyhedra with infinite, helical faces. In particular, there are no discrete chiral polyhedra with finite faces in addition to those described in Part I.