The connection between the 2d and 3d moves is a projection, right? You make a 2d slice through the 3d lattice, and then projet teh trajectory of the 3d piece on it. If you take the slice parallel to the cubic lattice coordinate planes, you get a normal chess board, and 3d bishops project to normal Bishops on it. As do Unicorns. The interesting quastion is what would happen if you do that with the haxagonal slice. Neither Bishops nor Unicorns move in the slice.
The connection between the 2d and 3d moves is a projection, right? You make a 2d slice through the 3d lattice, and then projet teh trajectory of the 3d piece on it. If you take the slice parallel to the cubic lattice coordinate planes, you get a normal chess board, and 3d bishops project to normal Bishops on it. As do Unicorns. The interesting quastion is what would happen if you do that with the haxagonal slice. Neither Bishops nor Unicorns move in the slice.