Intuition check--tiling a 3-sphere with 16 tetrahedra Lately I've been trying to understand/visualize the geometry of a 3-sphere (been hanging out in the cosmology section), and I think I'm getting it, at least to some extent. Intuitively, I think a 3-sphere can be tiled by 16 tetrahedra whose edges (and faces) meet at 90-degree angles. It seems "obvious" to me, and I can hand-wave an explanation for it, but I can't seem to find direct confirmation online (and, topology/geometry not being my field, I have no idea how to go about proving this in any mathematically sound manner). Can someone confirm that this works, or explain how one could show that it works, or correct me if my intuition has led me horribly astray? Many thanks!