Create dice marked with pips corresponding to the centers of the densest packing of circles in a square. 3 and 6 will be different from traditional.
Could optimize distance between dots on adjacent faces to choose the among the 4 possible orientations of a each face.
Instead of dots, compute the Voronoi partition of the face around the circle centers, then color the regions with as few colors as possible.
Apply to other dice used in gaming -- non-square faces, d10. The pattern could become difficult to recognize for large numbers.
Dominoes. 7 has a rattler: make the packing circle of the rattler as large as possible.