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Four Kinds of Rhombic Polyhedra

Four kinds of rhombic polyhedra are attached face to face in a single cluster: a prolate rhombohedron, a flat hexahedron, a rhombic dodecahedron, and a flat rhombic dodecahedron. The faces of these polyhedra are rhombi having diagonal ratio

and/or

, where

is the golden ratio.

The void inside the construction corresponds to a polar zonohedron.

Contributed by: Sándor Kabai

Show Initialization Code

(7 lines omitted)

Rhombohedron (Wolfram MathWorld)

Rhombic Dodecahedron (Wolfram MathWorld)

Polar Zonohedron (Wolfram MathWorld)

R. Towle, Zonohedral Completion (Wolfram Library Archive)

"Four Kinds of Rhombic Polyhedra" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/FourKindsOfRhombicPolyhedra/

Contributed by: Sándor Kabai

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