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 E 3 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 E 3. There exist several families of chiral
polyhedra of types {∞, 3} and {∞, 4} with infinite, helical faces. In particular, there are no …

Chiral polyhedra in ordinary euclidean space E 3 are nearly regular polyhedra; their
geometric symmetry groups have two orbits on the flags, such that adjacent flags are in
distinct orbits. This paper completely enumerates the discrete infinite chiral polyhedra in E 3
with finite skew faces and finite skew vertex-figures. There are several families of such
polyhedra of types {4, 6},{6, 4} and {6, 6}. Their geometry and combinatorics are discussed in
detail. It is also proved that a chiral polyhedron in E 3 cannot be finite. Part II of the paper will …