Can I assume the corner cells are deleted so you don't have to work out what to do with the diagonals there?
Yes, you can, and correctly so -- especially with the leapers! (I've seen others try to manage that mess, and those were just cubical boards. On a tesseract? No, thank you!)
If a pawn or spear find themselves on an Open face, there are two (or all four, on faces 6 and 19!) directions that are "toward" the enemy Home face; how do they move then?
That would be based on where on the face they are. If they're at the midpoint, it's player's choice (I probably should include that in the text).
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.
I tried to work out (but without paper) how many squares a rook attacks on an empty board. There are 12 faces that it reaches in each direction, but those overlap, I think four faces in common? So it should be 5*12*2-4-1=115 (that last being the rook's current cell)? What about the bishop, or nightrider?... Oh, I guess bishops aren't colorbound?
That math/geometry is a bit wild, and it's a bit late right now (for me).
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.
Is there a reasonable way to flatten this for displaying on a table/screen? (I suspect not, because of the forking of paths.)
You're correct, and that's only one reason; the nature of a tesseract makes it hard in general to lay it out in two dimensions. Someone could probably do a diagram showing the Home Faces and how they connect to the Territory Faces, and the latter to each other, for each side; how to extend that to the entire tesseract is another question entirely.
That said, I have seen people program 4D and even 5D Rubik's cubes, so it's probably possible.
Does the setup section's use of "clockwise" actually make sense?
Clockwise as seen by the player on the 2D board.
Now that I consider it, I probably should set up some kind of system where two corners are blacked-out and two are whited-out, to keep track of which corners are connected. That won't always be obvious.
Why alternate ordinary and berolina pawns? Doesn't that hurt pawn structures? (Does it just not matter on this wacky board?)
They should only run into each other in their early moves, and even then only if they make single moves at the start instead of double moves.
Personally, I think it doesn't so much hurt "pawn structures" as just make for different ones that would have to be worked out in play. That said, I don't think I'd do it that way on a board without this structure's unique flavors.
Yes, you can, and correctly so -- especially with the leapers! (I've seen others try to manage that mess, and those were just cubical boards. On a tesseract? No, thank you!)
That would be based on where on the face they are. If they're at the midpoint, it's player's choice (I probably should include that in the text).
I'm not sure I understand the question.
That math/geometry is a bit wild, and it's a bit late right now (for me).
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.
You're correct, and that's only one reason; the nature of a tesseract makes it hard in general to lay it out in two dimensions. Someone could probably do a diagram showing the Home Faces and how they connect to the Territory Faces, and the latter to each other, for each side; how to extend that to the entire tesseract is another question entirely.
That said, I have seen people program 4D and even 5D Rubik's cubes, so it's probably possible.
Clockwise as seen by the player on the 2D board.
Now that I consider it, I probably should set up some kind of system where two corners are blacked-out and two are whited-out, to keep track of which corners are connected. That won't always be obvious.
They should only run into each other in their early moves, and even then only if they make single moves at the start instead of double moves.
Personally, I think it doesn't so much hurt "pawn structures" as just make for different ones that would have to be worked out in play. That said, I don't think I'd do it that way on a board without this structure's unique flavors.