A 0/1-polytope is a convex polytope generated by the convex hull of a subset of coordinates value 0 or 1, . The full domain is the unit hypercube with cut hyperplanes passing through these coordinates. A -polytope requires at least vertices, and can't be all in the same hyperplanes.
simplex polytopes for example can be generated vertices, using the origin, and one vertex along each primary axis,, etc. Every simple 0/1-polytope is a Cartesian product of 0/1 simplexes.