Post #1868684
2026-02-07 11:14 UTC
Here's a bit of geometry I just learned that is relevant to board & video game design. In 2 dimensions there are exactly 3 regular tilings of the plane: triangles, squares and hexagons. In 3 dimensions there is exactly one: every 3-dimensional voxel game is necessarily made of cubes and so looks like minecraft. In 4 dimensions there are again 3 possibilities. In dimensions 5 and higher, hypercubes are again the only option. So interesting tilings exist only in dimensions 2 and 4.
https://en.wikipedia.org/wiki/List_of_regular_polytopes#Tessellations_of_Euclidean_4-space
Replies (3)
-
@OscarCunningham@mathstodon.xyz 2026-02-07 11:38
@julesh@mathstodon.xyz (https://oeis.org/A121273)
-
@metarecursive@mathstodon.xyz 2026-02-08 02:58
@julesh@mathstodon.xyz I've seen someone making a minecraft-like voxel game but using hexagonal blocks--the game takes place on a (ico)sphere and IIRC, they calculate the dual of their ico-sphere and leverage some math trickery I only vaguely followed to manage their hex-prisms spherical world.
-
@RuchiraSDatta@mathstodon.xyz 2026-02-08 04:01
@julesh@mathstodon.xyz However, one can have other 3d regular tilings with a small number of distinct types of polyhedra, not all the same one.