Definition:Equidecomposable Polyhedra

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