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Geometric relations

The cube is unique among the Platonic solids for being able to tile Euclidean space regularly. It is also unique among the Platonic solids in having faces with an even number of sides and, consequently, it is the only member of that group that is a zonohedron (every face has point symmetry).

The cube can be cut into 6 identical square pyramids. If these square pyramids are then attached to the faces of a second cube, a rhombic dodecahedronis obtained.

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Q: What are the Geometric relations of cube?
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