# 0/1-Polytopes in 3D

0/1-Polytopes in 3D

The convex hull of a set is the smallest convex set that contains . For instance, the convex hull of three distinct points is a triangle or a line segment.

S

S

A 0/1-polytope is the convex hull of a set of points with coordinates 0 or 1. In other words, a 0/1-polytope is the convex hull of a subset of vertices of a hypercube (the generalization of a cube to any number of dimensions).

A 3D cube has eight vertices, so it has =256 subsets of vertices. This Demonstration shows the corresponding 256 0/1-polytopes.

8

2