Single Comment

Colourbound. Obvious for Bishop and Ferz on squares, which have two bindings for them, dark and light. Hex has three bindings, because whatever hexagon your piece is on, there are three directions not two. Cubic has 3 planes and 6 standard diagonals, because opposite edges are one and the same diagonal, and there are 12 edges per starting cube. Cubic has 4 nonstandard diagonals because opposite corners are one and the same diagonal (going the opposite directions), and there are 8 corners (vertices). Bishop in cubic passing through edges the six ways possible can still never reach any cube sharing a face; therefore there are two bindings in cubic for Bishop. In other words, you'll need another Bishop to reach the other half of cubes. In nomenclature of piece-types, Unicorn is the nonstandard cubic-diagonal logical mover (triagonal) through vertices; and there are four bindings, as experimentation shows with a dozen blocks on your work table. This is more important stuff than Betza's Chess Unequal Armies for the 22nd century. Like proliferation itself, CUA has no possible logical end, whereas basics of colourboundness and bindings, divergence and symmetry, are being universally applicable on the 3 boards: hex, cubic, square. And therefore the best forms can eventually surface and all the rest, being infinite, scrapped into the dustbin of history.