I wish you good luck, and great fortune in finding a suitable opponent. I found it quite difficult, and finding the minimum number of pieces to force mate was even more difficult. Ben Reiniger put up with my fumbling around pushing pieces until I realized it required the lone king vs king and 2 major pieces from the 1 queen and 2 bishops (bishops and rooks essentially exchanging roles when going from FIDE to my 4D game) and a specific alignment of the 4 pieces, which can also be forced. The advantage to my method is that it demonstrates a forced mate on any-sized 2D boards. Most 4D games cannot do that. Once you get past a 5x5 2D board, you can no longer use the trick of putting your king in the middle of the gameboard and then using a ridiculously powerful 4D queen placed between your king and the opponent's king to pin that king against the side of the board in mate. If the 2D boards are 6x6 or larger, that tactic does not work, because the opponent king has another row of squares to which it can retreat and get out of check.
Build the playspace. Make at least 1 physical board so you can push pieces. A physical game makes things more real. I believe using a physical board makes teaching and learning at least a little bit easier. And with 4D variants, the easier you can make it, the better, unless your goal is for no one to ever play the game. However, making a physical game for demo and experimenting with is worthwhile, I've found. Sometimes you can suck people into making a few moves in the game. And when you have physical components, you can use anything else you have handy to look at ideas far afield from chess.
I've found that the basic 4D board has uses in many games besides chess. I've designed a wargame, a trading game, and an empire-building game, a "3X" game, not quite a 4X game since all points on the board are already known at the beginning of the game so there is no eXploration, just eXpansion, eXploitation, and eXtermination. All of these games are played on a "simple 4D board". I don't necessarily tell people that when they first play. But they should notice that on a larger than normal board, it is rather easy to get from any one location on the board to any other. There are more ways to get from here to there than in 2D or 3D.
I wish you good luck, and great fortune in finding a suitable opponent. I found it quite difficult, and finding the minimum number of pieces to force mate was even more difficult. Ben Reiniger put up with my fumbling around pushing pieces until I realized it required the lone king vs king and 2 major pieces from the 1 queen and 2 bishops (bishops and rooks essentially exchanging roles when going from FIDE to my 4D game) and a specific alignment of the 4 pieces, which can also be forced. The advantage to my method is that it demonstrates a forced mate on any-sized 2D boards. Most 4D games cannot do that. Once you get past a 5x5 2D board, you can no longer use the trick of putting your king in the middle of the gameboard and then using a ridiculously powerful 4D queen placed between your king and the opponent's king to pin that king against the side of the board in mate. If the 2D boards are 6x6 or larger, that tactic does not work, because the opponent king has another row of squares to which it can retreat and get out of check.
Build the playspace. Make at least 1 physical board so you can push pieces. A physical game makes things more real. I believe using a physical board makes teaching and learning at least a little bit easier. And with 4D variants, the easier you can make it, the better, unless your goal is for no one to ever play the game. However, making a physical game for demo and experimenting with is worthwhile, I've found. Sometimes you can suck people into making a few moves in the game. And when you have physical components, you can use anything else you have handy to look at ideas far afield from chess.
I've found that the basic 4D board has uses in many games besides chess. I've designed a wargame, a trading game, and an empire-building game, a "3X" game, not quite a 4X game since all points on the board are already known at the beginning of the game so there is no eXploration, just eXpansion, eXploitation, and eXtermination. All of these games are played on a "simple 4D board". I don't necessarily tell people that when they first play. But they should notice that on a larger than normal board, it is rather easy to get from any one location on the board to any other. There are more ways to get from here to there than in 2D or 3D.
Happy designing!