How knights move in 4D
We all know the popular game of Chess, but many people still ask,
Traditionally the knight moves like an "L", or 3 spaces in one direction and only 1 in another, jumping over any pieces on the way.
You may have noticed that every time the knight moves the color it's on always changes, from white to black and black to white, this is similar to moving a rook just one tile up/down/left/right.
So maybe from the perspective of the knight it only moves one space in it's own dimension and every other piece moves weird instead?
Let's start with a
Now the board changes, only a few squares are accessible with the moves we currently have available and the knight can only move up, down, left or right in his dimension, which is equivalent to standard knight moves.
Going up to 3D
Looks good, but not every square is accessible yet, let's add another dimension, this will represent another 2 movement options for the knight. This brings us up to 3D.
The highlighted square is
However, this isn't exactly accurate, you may notice the perfectly flat side on the top (and bottom), this is because this board isn't connected properly.
This doughnut shaped board is far more accurate. It's just the board seen above, but bent a bit to make the top and bottom touch, each square can still only hold one piece and is perfectly flat from the knight's point of view.
You may be saying that this is "heresy" or "cursed", but many variants (like Hexagonal chess or Circular chess) change the shape of the board in order to fit their needs.
4D chess
So just expand the "cubes" into 4D hypercubes, make some more connections between the spaces by bending and stretching them. It should be trivial enough for you to imagine the full 4D shape on your own in your head, I will leave you to it.
Now you know what to say when someone asks: