[For part I see the review above.] The first section summarizes Part I, giving particular attention to the 3-dimensional point groups. The second section establishes subgroup relationships among the various irreducible reflection groups in 4 dimensions: 5 finite and 5 infinite. The third gives presentations for many of the 4-dimensional point groups, crystallographic and non-crystallographic. The fourth shows how a large family of uniform polytopes and honeycombs can be represented by graphs with rings drawn round certain nodes: a notation which facilitates the determination of numerical properties such as the number of edges at each vertex. The fifth shows how to find coordinates for the vertices of each such polytope, including new 5-dimensional coordinates for the 600-cell and 120-cell. The sixth extends these results to honeycombs. The seventh considers the orbit of a point for the rotatory subgroup of a reflection group, and determines in which cases the points so obtained are the vertices of the uniform polytope or honeycomb. The ''grand antiprism'' described in the final section is unique among 4-dimensional uniform polytopes in that it cannot be obtained by either of the constructions already considered.