Published online by Cambridge University Press: 01 August 2016
The first part of this article covers some well-known ground in preparation for the second part on the Archimedean honeycomb duals. Mathematically speaking some of this second part is, so far as I know, no more than conjecture: I do not myself know of a proper systematic approach to such honeycombs.
As far as possible I have used names for the polyhedra from standard references (e.g. [1]). But references vary, and I have not found all of them described. In such cases I have tried to choose names which are appropriate and technically correct.