 Hypercube

Ciro Santilli 34  Updated 2024-12-15  +Created 1970-01-01

square, cube. 4D case known as tesseract.

Convex hull of all

{- 1, 1}^{D}

(Cartesian product power) D-tuples, e.g. in 3D:

( 1,  1,  1)
( 1,  1, -1)
( 1, -1,  1)
( 1, -1, -1)
(-1,  1,  1)
(-1,  1, -1)
(-1, -1,  1)
(-1, -1, -1)

From this we see that there are

2^{D}

Two vertices are linked iff they differ by a single number. So each vertex has D neighbors.