Mx. Chara Aznable of Pnictogen on Nostr: Hm is there any value in trying to work up a scheme for representing 3D space as ...

Hm is there any value in trying to work up a scheme for representing 3D space as filled with rhombic dodecahedra instead of cubes? I was thinking of how one might try to implement a 3D grid that has some advantage in analogy to the hexagonal grid in representing 2D space. A plain square grid has a subtle problem in defining the "neighborhood" of a cell, for there are four face-to-face members and four corner-to-corner members whereas the hexagonal cell has six identical neighbors.

I trawled through MathWorld looking up polyhedra that tessellate 3D space. There's a lot of weird choices but only the rhombic dodecahedron, so far as I can tell, is both convex and has all its faces congruent, all the same shape.

I'm sort of curious generally about the subtle issues that crop up in simulations because of the limitations on how a continuous *field* of some sort, in 2D or 3D space, can be divided up into discrete units. #Programming culture being what it is, it's tended to overuse rectilinear models because they're so easy to implement and there must be a lot of software out there where square or cubical grids are deemed *good enough* even if really they aren't.

(cont'd)