Chord cubes and the 7-limit diamond

One of the most salient features of the 7-limit tonality diamond is
that it is one of the two types of 2x2x2 chord cubes. If we center the
cube on [-1/2,-1/2,-1/2], so that the chords are [i,j,k] as i, j and k
range between -1 and 0, we get the diamond. If we center on
[1/2,1/2,1/2], which is what I've been doing, then the cube is the
stellated hexany.

Hence, one obvious means of getting larger scales containing diamonds
(or stellated hexanies, for that matter) is via chord cubes. For
instance, the 3x3x3 otonal-centered chord cube, with 32 notes, or 31
notes if we breed reduce, which I wrote Bodacious Breed in.