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Math Help - Number of neighbours of a tetrahedron?

  1. #1
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    Number of neighbours of a tetrahedron?

    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...
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  2. #2
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    Quote Originally Posted by Unenlightened View Post
    I'm wondering how many "neighbours" a tetrahedron would have in a tessellation of R^3.
    Problem is you can't tesselate \mathbb{R}^3 with tetrahedra (at least, not regular ones)...
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