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Constructing a Rhombic Hexecontahedron with Zometool

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Zometool, a construction set consisting of connector balls and struts, can be used to build elaborate geometric structures.

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How many Zome balls are needed to create a rhombic hexecontahedron (RH)?

- 12 at the vertices of an icosahedron (ICO)

- 30 at the vertices of an icosidodecahedron (ID)

- 20 at the vertices of a dodecahedron (DOD)

- 1 at the center

Together with the central node and the central struts, the RH can also be also modeled as an assembly of 20 golden rhombohedra. The edge lengths of the three associated polyhedra have proportions equivalent to those of the Zometool struts. If the length of an ICO edge is 1, then the length of an ID edge is also 1, which is the short diagonal of the golden rhombus of an RH.

Red struts connect the pentagonal receptacles, while the blue struts connect the rectangular receptacles.

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Contributed by: Sándor Kabai (August 2022)
Open content licensed under CC BY-NC-SA

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