Dissection of the Oblate Golden Rhombohedron

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.