Casino dice with sharp edges are fair, but the cubes don't roll very well unless flung with considerable velocity on a special table as done in craps. Rounding off the edges and corners makes them roll better for tabletop games, but it is hard (probably impossible) to round all the edges in precisely the same way to keep a die fair.
Seek the best of both worlds by creating a casino-style die using a polyhedron with a larger dihedral angle. The rhombic triacontahedron (30 faces) seems attractive because with repeated numbers it can simulate a d6 or a d10.
This seems partially already done by GameScience precision dice, but they fail to have the face markings carved out then filled with paint of identical density, as casino dice do. Also, another problem of irregular shape found in testing.
Dihedral angles:
- cube 90
- octahedron 109
- dodecahedron 117
- rhombic dodecahedron 120
- icosahedron 138
- rhombic triacontahedron 144
Based on dihedral angle considerations only (so one needs both edge transitivity and face transitivity), for d12, one should prefer rhombic dodecahedral dice if you want them to roll more, or regular dodecahedral dice if you want them to roll less.
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