Rhombic Hexecontahedron in a Rhombohedron

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Find a point that divides the diagonal of a large rhombohedron in proportion to the golden ratio. Construct a small rhombohedron around this point so that one of its vertices coincides with the center of . Construct a rhombic hexecontahedron so that one of its constituent 20 rhombohedra coincides with . If you enlarge the , then you will see two small dots on each face of , which are actually vertices of the . (Drag to rotate the graphic to see the dots.) Therefore, vertices (out of 20) of the are on the six faces of . When 20 rhombohedra with s inside them are assembled to form a large , then the s meet at their vertices, and a rhombic triacontahedron connected face-to-face can be inserted between them.

Contributed by: Sándor Kabai (October 2015)
With additional contribution by: István Muzsai
Open content licensed under CC BY-NC-SA




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