Dissection of the Oblate Golden Rhombohedron

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This Demonstration shows a dissection of the oblate golden rhombohedron into two prolate golden rhombohedra and an oblate golden rhombohedron, which are smaller by a factor of (the golden ratio).

Contributed by: Anja Komatar (March 2011)
Problem proposed by: Izidor Hafner
Open content licensed under CC BY-NC-SA



If the oblate golden rhombohedron has volume 1, then the prolate golden rhombohedron has volume and the oblate golden rhombohedron whose edges are times as long has volume . So there exists a dissection of O6 to one O6 and two A6 (see the Demonstration in Related Links). The basic idea is to dissect three smaller rhombohedra to a parallelepiped with the same height and angles as two smaller prolate rhombohedra and then to dissect the parallelepiped to the larger oblate rhombohedron.

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