4d cube

5

Constructing a Tesseract

The vertices of an n-dimentional analogue of a square (aka a point, line, cube, tesseract, etc.) can be labeled with n-bits in base-2. So if we label the vertices of a cube (a 3-dimentional analogue of a square) we use three bits of binary. We label the vertices such that there is only a 1-bit difference between the labels of any two connected points. We can use this knowledge to easily draw a tesseract.

1. Draw 16 points. They don’t have to be in any order, but this works best if they are arranged like the vertices of two cubes next to each other.

2. Label the vertices using 4 binary bits. This can be done by labeling the two cubes using 3 bits, then adding a 1 to the beginning of every vertex on one cube, and a 0 on the other.

3. Connect each point where the two labels differ by only one bit.

4. Admire the binary.