# 0/1-Polytopes in 3D

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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.

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Contributed by: George Beck (June 2014)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

In 2D, there are four vertices and convex sets; in 4D, the hypercube has 16 vertices, so there are convex hulls. Neither the 2D nor 4D case is shown here. The 2D case is too easy; the 4D examples would be interesting to project into 3D, say into the 3-space orthogonal to the vector .

Reference

[1] H. Ziegler, *Lectures on Polytopes*, New York: Springer, 1995 pp. 19–22.

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