Is there an easy way to map a sphere onto a dodecahedron? I'm playing with the idea of generating "planet dice."
I've been thinking of ways to make a projection of a planetary map onto a die for the purposes of using it as a pencil and paper RPG prop. It seems to me that a d6/cube would be too few surfaces and not quite satisfyingly round and a d20/icosahedron would result in small hard-to-read surfaces. Also, a lot of gaming stuff already comes optimized for hex maps.
I actually know for sure this is possible, because I've found a page with map projections.
(And Thinkgeek did a icosahedron
(though it does not look rollable.)
That's about exactly what I want to do, but I'm trying to work out how I would do something like that myself. From the standpoint of the Earth, I might like to experiment with rotation to see the best arrangement of vertices against interesting surface areas, or even give Pangaea a shot. If that worked out, then doing the moon or fictional planets would a next step.
Is there any good existing mapping software for something like this or am I better off trying to do my own math? Are there good open-source maps of, say, Traveler planets, that could be used for practice?