If you tile R^2 with squares, each square has 8 "neighbours" - 1 at each edge, and 1 at each vertex that does not share an edge.
If R^2 is tiled with equilateral triangles, each triangle touches12 other triangles around it.
In R^3 each cube would touch 26 others - 6 would share a face with it, 12 an edge but not a face, and 8 only a vertex.
I'm wondering how many "neighbours" a tetrahedron would have in a tessellation of R^3.
Any suggestions?
Of course, if I had a bunch of tetrahedra lying around that I could stick together and physically count, that would be fine... but I don't...