Hill tetrahedron

In geometry, the Hill tetrahedra are a family of space-filling tetrahedra. They were discovered in 1896 by M. J. M. Hill, a professor of mathematics at the University College London, who showed that they are scissor-congruent to a cube.

For every ${\displaystyle \alpha \in (0,2\pi /3)}$, let ${\displaystyle v_{1},v_{2},v_{3}\in {\mathbb {R}}^{3}}$ be three unit vectors with angle ${\displaystyle \alpha }$ between every two of them. Define the Hill tetrahedron ${\displaystyle Q(\alpha )}$ as follows:

...
Wikipedia