In the 15th-century manuscript De quinque corporibus regularibus, Piero della Francesca includes a drawing of an octahedron circumscribed around a cube, with eight of the cube edges lying in the octahedron's eight faces. Three cubes inscribed in this way within a single octahedron would form the compound of three cubes, but della Francesca does not depict the compound.[4]
This compound can be constructed by superimposing three identical cubes, and then rotating each by 45 degrees about a separate axis (that passes through the centres of two opposite faces).[3]
^Verheyen, Hugo F. (1996), "Chapter 4: Classification of the finite compounds of cubes", Symmetry Orbits, Design Science Collection, Boston: Birkhäuser, pp. 95–159, doi:10.1007/978-1-4612-4074-7_5, ISBN0-8176-3661-7, MR1363715; see in particular p. 136.
^Brückner, Max (1900), Vielecke und Vielflache, Theorie und Geschichte, Leipzig: B.G. Teubner, Plate 23