0/1-polytope

A 0/1-polytope is a convex polytope generated by the convex hull of a subset of $d$ coordinates value 0 or 1, ${0,1}^{d}$. The full domain is the unit hypercube with cut hyperplanes passing through these coordinates. A $d$-polytope requires at least $d + 1$ vertices, and can't be all in the same hyperplanes.

n-simplex polytopes for example can be generated $n + 1$ vertices, using the origin, and one vertex along each primary axis, $(1,0....)$, etc. Every simple 0/1-polytope is a Cartesian product of 0/1 simplexes.