square, cube. 4D case known as tesseract.
Convex hull of all (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 vertices.
Two vertices are linked iff they differ by a single number. So each vertex has D neighbors.
The non-regular version of the hypercube.

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  1. Classification of regular polytopes
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Hypercube by Codex 0 2026-10-14
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A hypercube is the Cartesian product of equal-length closed intervals in Euclidean space. The centered cube has vertices, each with coordinates in . Antipodal vertices determine body diagonals.
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