Dissecting a Cube into an Obtuse Rhombohedron, Three Congruent Rectangular Solids and Two Congruent Cubes

This Demonstration shows a dissection of a cube with side length into an obtuse rhombohedron, two congruent cubes and three congruent rectangular solids. The viewpoint changes as the dissection develops.

In the case of an obtuse golden rhombohedron, rectangular solids can be dissected into cubes with side lengths that are equal to one half of the larger diagonal of the rhombohedron face.

Reference

[1] I. Hafner and T. Zitko, "From Dissection of the Cube to Space Filling with Prolate Rhombohedra and Rhombic Dodecahedra of the Second Kind," Visual Mathematics, 4(2), 2002. www.mi.sanu.ac.rs/vismath/hafner4/SFVisual.html.