I have a pile of uniform cuboids, of side a,b,c. I would like to make a regular cube. The sides are not in harmonic ratio ( cf. de Bruijn) but are in fact white sugar lumps.
The minimum regular cube I can envisage is of side a+b+c. I have experimented making a 3x3x3 cube of 27 cuboids using a 3x3x3 magic cube to direct operations but find that
- I get a non tight pack on 2 out of 3 levels
- I cannot make a 3rd level that is compatible with the first two, one cuboid has to be omitted from the arrangement.
It seems more likely that I should be using a 6x6x6 magic cube formulation to match the 6 orientations of the cuboids a.b, b.a, a.c, c.a, b.c, c.b. But while I can visualise a 3x3x3 I would need to know how to encode the cells of a published 6x6x6 cube into these 6 possible cuboid orientations.
Any thoughts are appreciated