Category:Equidecomposable Polyhedra

This category contains results about Equidecomposable Polyhedra.
Definitions specific to this category can be found in Definitions/Equidecomposable Polyhedra.

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:

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