\begin{definition}[Definition:Dual Polyhedron]
Let $P$ be a polyhedron.
The '''dual polyhedron''' $D$ of $P$ is the polyhedron which can be constructed as follows:
:$(1): \quad$ The vertices of $D$ are the centroids of the faces of $P$.
:$(2): \quad$ For each edge of $P$ which is adjacent to two faces $F_1$ and $F_2$ of $P$, an edge of $D$ is constructed which is adjacent to the vertices of $D$ forming the centroids of $F_1$ and $F_2$.
\end{definition}