Definition:Dual Polyhedron

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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 $F_2$.