next up previous contents
Next: What is simple/simplicial polytope? Up: Convex Polyhedron Previous: What is simplex?   Contents

What is cube/hypercube/cross polytope?

A subset $ P$ of $ R^d$ is called a unit $ d$-cube if it is the convex hull of all $ 2^d$ points with components 0 or $ 1$. It has exactly $ 2^d$ vertices and $ 2 d$ facets. A cube or hypercube is a convex polytope which is isomorphic to the $ d$-cube for some $ d$.

A dual (see 2.4) of a cube is called a cross polytope.

Komei Fukuda 2004-08-26