Apologies for the confusion; I had misremembered what I worked out years ago, and didn't spend much time checking how my thoughts aligned with the Red Blob site I linked.
When I've done this before, I project down along one triagonal, and the result is a hexagonal grid, but not with the "cubic coordinates" of the Red Blob site. Instead, you get coordinates whose sum is 0, 1, or 2 (any other sum in the cube coordinates get projected down to one of these, depending on its remainder mod 3), and those correspond to the 3-coloring of the hex grid. Under this projection, if my doodling just now is correct, cubic rooks are hex rooks; cubic bishops are hex rook+bishop; cubic unicorns are hex dabbabah+null-move.
That aside, I would still argue that Gilman isn't wrong in anything, but takes different definitions and reaches different conclusions. We've had games here on non-regular tesselations, and differences of opinions arise when trying to think more-topologically or more-geometrically.
Apologies for the confusion; I had misremembered what I worked out years ago, and didn't spend much time checking how my thoughts aligned with the Red Blob site I linked.
When I've done this before, I project down along one triagonal, and the result is a hexagonal grid, but not with the "cubic coordinates" of the Red Blob site. Instead, you get coordinates whose sum is 0, 1, or 2 (any other sum in the cube coordinates get projected down to one of these, depending on its remainder mod 3), and those correspond to the 3-coloring of the hex grid. Under this projection, if my doodling just now is correct, cubic rooks are hex rooks; cubic bishops are hex rook+bishop; cubic unicorns are hex dabbabah+null-move.
That aside, I would still argue that Gilman isn't wrong in anything, but takes different definitions and reaches different conclusions. We've had games here on non-regular tesselations, and differences of opinions arise when trying to think more-topologically or more-geometrically.