Intuition check-tiling a 3-sphere with 16 tetrahedra

[cephron]

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!

 

[Tinyboss]

It's usually referred to as "triangulation" rather than "tiling". Here's a link that may be helpful: http://theory.org/geotopo/3-sphere/html/node5.html#SECTION00052000000000000000

 

[cephron]

Thank you, Tinyboss! That's exactly what I was looking for. I had been googling with the wrong terminology.