“An imaginary cube is a three-dimensional object which has square projections in three orthogonal directions, just as a cube has” — Hideki Tsuiki

A cube projects square shadows in 3 orthogonal directions that are parallel to its sides. But there are many other 3D objects that have this same property. Hideki Tsuiki named these objects Imaginary Cubes and studied their properties.

I provide here a complete set of representatives of the 16 families of Minimal Convex Imaginary Cubes (as described by Hideki Tsuiki). You can arrange any combination of these imaginary cubes recursively, so they form a bigger compound imaginary cube (see the attached example of such arrangements).

I also provide an easy-to-print puzzle by Hideki Tsuiki called 3H = 6T (all 9 pieces will fit in a 6x6x6 cm box) and the parametric OpenScad script used to generate these models.

Further information:

• Hideki Tsuiki — Imaginary Cubes and Their Puzzles — Algorithms 2012, 5(2), 273-288 https://doi.org/10.3390/a5020273