Dissection of the Oblate Golden Rhombohedron
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).
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.