Cube in a Cube or the Intersecting Tetrahedra

A polyhedron compound of two cubes is obtained by allowing two cubes to share opposite polyhedron vertices, and then rotating one a sixth of a turn about the axis that joins the two opposite vertices (see fig. 1 below).

As you can see from fig. 2, the two-cube compound is made up of 12 pyramidal modules. Each pyramidal module is composed of two right triangles with ratio 2:1 and one isosceles right triangle.

Cube in Cube

Print the PDF with the paper model (shown in fig. 3) to make your own compound of two cubes.

Read more: from MathWorld.

Origami Variant
2-cube compoundDavid Brill devised an original way to make the compound of two cubes by using modular origami folding technique. You will need 12 square papers, 6 of one color + 6 of another, and a lot of patience to build your polyhedron compound.

Source: origami instructions found in Dave’s book: Brilliant Origami.