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What is simplex?

A subset $ P$ of $ R^d$ is called a $ k$-simplex ( $ k =0,1, 2, \ldots$) if it is the convex hull of $ k+1$ affinely independent points. It has exactly $ k+1$ vertices and $ k+1$ facets. A simplex is a $ k$-simplex for some $ k$.

Simplices are selfdual, i.e. a dual (see 2.4) of a simplex is again a simplex.

Komei Fukuda 2004-08-26