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](https://en.wikipedia.org/wiki/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.

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Also I think I could have started differently with this other [tetrahedron](https://en.wikipedia.org/wiki/Tetrahedron):

* $\{ (0,0,0), (1,1,0), (0,1,1), (1,0,1) \}$

[![enter image description here](https://i.stack.imgur.com/TV327.gif)](https://i.stack.imgur.com/TV327.gif)

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.