Building on 12 Polar Zonohedra

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Various rhombic polyhedra are used to build a structure around 12 polar zonohedra to fill space. The polar zonohedra have five zones and are bordered by rhombuses with a diagonal ratio that is equal to the golden ratio squared and rhombuses with a diagonal ratio that is equal to the square root of two. The constituent polyhedra also have the same rhombuses. The structure is shown in 13 stages.

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



Two kinds of rhombohedra and rhombic dodecahedra are used in the structure. The structure can be seen during the building or dismantling sequence, or by randomly selecting an intermediate stage. The structure can be used as a design for a geometrical sculpture. The stages and the entire structure can be built with Zometool.

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