The correspondence between 3D and Hex in the link is indeed not with the Cubic lattice, but with the Rhombic‐Dodecahedral one — what Gilman terms ‘Xyrixa’ (after an obscure variant of the same name) — equivalent to considering a single bishop binding of a cubic lattice in the same way that a single B binding on squares gives another square board. Thus Cubic B moves correspond to Hex/Xyrixa R moves, Cubic (2,1,1) leaps (‘Sexton’ leaps, per Punning by Numbers) to the other Hex radial, and Dabbaba leaps to Xyrixa B moves (which move off the Hex plane).
Additionally, a Sexton leap can be achieved by two Unicorn steps at right angles, as can a B step by two R steps, and the Cubic unicorn step is reachable by one R step and a perpendicular B step, as is the Hex ‘unicorn’ step on a Xyrixa board (≡ a Sexton leap by B step and perpendicular D leap). Hence an argument for unifying the two.
Of course, there is one major difference: the Hex move is arguably distinct in being not a Step, like the three Cubic radials, but a Leap like the cubic Sexton (in the sense that the cells such a move connects are not geometrically adjacent).
H.G.:
the diagonal slice through the cubic lattice does not produce a board of hexagons
Not, I imagine, the worst possible board for a CV: the R moves are zigzaggy but equivalent to cubic ones, and the (proper) bishop takes (standard) diagonals — but only half of them.
The correspondence between 3D and Hex in the link is indeed not with the Cubic lattice, but with the Rhombic‐Dodecahedral one — what Gilman terms ‘Xyrixa’ (after an obscure variant of the same name) — equivalent to considering a single bishop binding of a cubic lattice in the same way that a single
Bbinding on squares gives another square board. Thus CubicBmoves correspond to Hex/XyrixaRmoves, Cubic (2,1,1) leaps (‘Sexton’ leaps, per Punning by Numbers) to the other Hex radial, and Dabbaba leaps to XyrixaBmoves (which move off the Hex plane).Additionally, a Sexton leap can be achieved by two Unicorn steps at right angles, as can a
Bstep by twoRsteps, and the Cubic unicorn step is reachable by oneRstep and a perpendicularBstep, as is the Hex ‘unicorn’ step on a Xyrixa board (≡ a Sexton leap byBstep and perpendicularDleap). Hence an argument for unifying the two.Of course, there is one major difference: the Hex move is arguably distinct in being not a Step, like the three Cubic radials, but a Leap like the cubic Sexton (in the sense that the cells such a move connects are not geometrically adjacent).
H.G.:
Unless you do this :)
Not, I imagine, the worst possible board for a CV: the
Rmoves are zigzaggy but equivalent to cubic ones, and the (proper) bishop takes (standard) diagonals — but only half of them.