Definition:Equidecomposable Polyhedra
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Definition
Let $n \in \N$ be a natural number.
Let $K_1$ and $K_2$ be polyhedra embedded in a Euclidean space of $n$ dimensions such that both are the union of a finite number of $n$-simplexes
Let $K_1$ and $K_2$ be the union of a finite number of polyhedra:
\(\ds K_1\) | \(=\) | \(\ds A_1 \cup A_2 \cup \cdots \cup A_k\) | ||||||||||||
\(\ds K_2\) | \(=\) | \(\ds B_1 \cup B_2 \cup \cdots \cup B_k\) |
where:
- each pair of the polyhedra $A_i$ and $A_j$, and $B_i$ and $B_j$, intersect only in $m$-simplexes where $m < n$
- each $A_i$ is congruent to its corresponding $B_i$.
Then:
- $K_1$ and $K_2$ are equidecomposable
Also see
- Results about equidecomposable polyhedra can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): equidecomposable
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): equidecomposable