This is my favorite 2d view of a 4-dimensional cube, because it’s the most symmetrical. The 4 dimensions are depicted as going north, east, northeast and northwest.
Puzzle: count the cubes in this picture.
The cubes are a bit distorted, of course: they have to be because we’re squashing 4 dimensions down to 2! But they’re not very distorted.
Here’s the same picture rotated a bit, drawn by Tilman Piesk:
If we like, we can draw a 2d perspective picture of a 4-cube that’s so vivid it really looks 3-dimensional. There are lots of ways to do this. One clever way is to make the fourth dimension point inwards, towards the center:
This was drawn using Robert Webb’s Stella software, perhaps by Webb himself. I like the steel rods and brass balls.
On Wikicommons, someone who goes by the name “Maninthemasterplan” took another approach:
Cross your eyes so…
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