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
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Details
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.
Permanent Citation
A Dissection of a Prolate Golden Rhombohedron
Izidor Hafner and Anja Komatar
Dissecting a Rhombohedron into Two Congruent Rhombohedra
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Dissection of a Rhombohedron into a Right Prism with the Same Base
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Equidecomposition of a Rhombohedron, Hexagonal Prism, and a Rhombic Dodecahedron
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Two Solids Made from Golden Rhombic Solids
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Dissection of Two Stellated Dodecahedra
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26-Piece Dissection of a Cube
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Dissection of Three Polyhedra into Two
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Dissection of a Prismatoid into Prisms
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