Direct product Updated +Created
A Cartesian product that carries over some extra structure of the input groups.
E.g. the direct product of groups carries over group structure on both sides.
Hypercube Updated +Created
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.