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.
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.