I'd start here... https://en.wikipedia.org/wiki/Dice The 'fair' ones are... Platonic solids, the five regular polyhedra: 4, 6, 8, 12, 20 sides then the less 'fair' ones... Catalan solids, the duals of the 13 Archimedean solids: 12, 24, 30, 48, 60, 120 sides Bipyramids, the duals of the infinite set of prisms, with triangle faces: any even number above 4, and usually divisible by 4 so that a face will face up Trapezohedrons, the duals of the infinite set of antiprisms, with kite faces: any even number above 4 Disphenoids, an infinite set of tetrahedra made from congruent non-regular triangles: 4 sides So you need to determine the shape of the 'fairest' facets for any number of facets you propose... Once you have done that there's som Math to determine their angles and so on... Here's some more info on 'irregular but fair' dice... http://mathoverflow.net/questions/46684/fair-but-irregular-polyhedral-dice