We say that two polyhedra $P$ and $Q$ are scissor-equivalent if there exists a finite number $P_{1},\ldots,P_{N}$ of polyhedra and $\theta_{1},\ldots,\theta_{N}$ isometries such that

1. 1.

   $P=\bigcup_{{k=1}}^{N}P_{k}$ and $Q=\bigcup_{{k=1}}^{N}\theta_{k}(P_{k})$;

2. 2.

   $P_{j}\cap P_{k}$ and $\theta_{j}(P_{j})\cap\theta_{k}(P_{k})$ have empty interior for every $k\neq j$