Playing on the 2d surface has the nicety of rook lines still actually restricting the enemy king into one side or the other. What does mating material look like here?
I'm not sure I understand the question.
For starters, can two rooks force mate against a lone king? If the corners weren't removed I think they could. Two queens probably suffice? Maybe it's best to see if this has been resolved on the surface of a 3D cube first...
But yes, the Bishops are not colorbound, strictly speaking. It's not possible, on a cube's corner (much less a tesseract's), to have a colorbound check pattern. I didn't realize that when I put four on each side, but then I decided that it wasn't that big of a deal; switching is a trick that requires rounding a corner.
I'd like to try to work out a bishop's path (and number of attacked squares) partly for this reason: it might be possible to effectively wrap around corners by going the long-long way around?...
Clockwise as seen by the player on the 2D board.
But I'm not sure that makes sense, in the same way that clockwise isn't unambiguous in 3D: it depends on from which side of the surface you're looking.
For starters, can two rooks force mate against a lone king? If the corners weren't removed I think they could. Two queens probably suffice? Maybe it's best to see if this has been resolved on the surface of a 3D cube first...
I'd like to try to work out a bishop's path (and number of attacked squares) partly for this reason: it might be possible to effectively wrap around corners by going the long-long way around?...
But I'm not sure that makes sense, in the same way that clockwise isn't unambiguous in 3D: it depends on from which side of the surface you're looking.