Here is a nice version of the periodic table (produced jointly by the Association for the British Pharmaceutical Industry, British Petroleum, the Chemical Industry Education Centre, and the Royal Society for Chemistry) that focuses on the applications of each of the elements, rather than their chemical properties. A simple idea, but remarkably effective in bringing the table to life.
It might be amusing to attempt something similar for mathematics, for instance creating a poster that takes each of the top-level categories in the AMS 2010 Mathematics Subject Classification scheme (or perhaps the arXiv math subject classification), and listing four or five applications of each, one of which would be illustrated by some simple artwork. (Except, of course, for those subfields that are “seldom found in nature”. :-) )
A project like this, which would need expertise both in mathematics and in graphic design, and which could be decomposed into several loosely interacting subprojects, seems amenable to a polymath-type approach; it seems to me that popularisation of mathematics is as valid an application of this paradigm as research mathematics. (Admittedly, there is a danger of “design by committee“, but a polymath project is not quite the same thing as a committee, and it would be an interesting experiment to see the relative strengths and weaknesses of this design method.) I’d be curious to see what readers would think of such an experiment.