# Definition:Simplex

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## Contents

## Definition

A **simplex** is an $n$-dimensional generalization of a triangle and tetrahedron, for $n \in \Z_{>0}$.

A $k$-simplex is a $k$-dimensional polytope which is the convex hull of its $k + 1$ vertices.

## Also see

## Linguistic Note

The plural of **simplex** is **simplices**, pronounced ** sim-pli-seez**.

Compare the plural forms of **vertex**: **vertices** and **index**: **indices**.

## Sources

- 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $5$

- Weisstein, Eric W. "Simplex." From
*MathWorld*--A Wolfram Web Resource. http://mathworld.wolfram.com/Simplex.html