I was presented with the problem of breaking the unit cube $[0,1] \times [0,1] \times [0,1] $ into tetrahedron shapes. The first two pieces are easy, but it's not so easy to visualize after that. I found:
$\{ (0,0,0), (1,0,0), (0,1,0), (0,0,1) \}$
$\{ (1,1,1), (1,1,0), (1,0,1), (0,1,1) \}$
What remains is a triangular prism. Then maybe I think it readily splits into 2 or 3 pieces. In any case, they are difficult to draw and keep track of all the data.
Also I think I could have started differently with this other tetrahedron:
- $\{ (0,0,0), (1,1,0), (0,1,1), (1,0,1) \}$
There should be lots of solutions, but I neither have the date to store into a computer nor do I have picture of even a single one.
[Computational Geometry]
$\endgroup$ – john mangual Mar 28 '18 at 14:41