Question 117
How many ways are there to cut a cube $S$ into tetrahedra $\{T_1, \dots, T_k\}$ with the following properties?
(1) Every vertex of $T_1, \dots, T_k$ is one of the vertices of $S$.
(2) For every $i \neq j$, the intersection of $T_i$ and $T_j$ is a common face of them, a common edge of them, a common vertex of them or empty.
(1) Every vertex of $T_1, \dots, T_k$ is one of the vertices of $S$.
(2) For every $i \neq j$, the intersection of $T_i$ and $T_j$ is a common face of them, a common edge of them, a common vertex of them or empty.