Construction of Rhombic Dodecahedron
Theorem
The rhombic dodecahedron can be constructed as follows:
Take a cube $K$ embedded in $3$-dimensional space.
Place $6$ more cubes, each congruent with $K$, so that one face of each coincides with a different face of $K$.
Join the vertices of $K$ to the centers of the adjacent cubes to describe square pyramids whose apices are the centers of the adjacent cubes and whose bases are the faces of $K$.
The polyhedron formed by the $6$ square pyramids so formed, together with $K$, is a rhombic dodecahedron.
Proof
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