Definition:Vertex of Simplex

Definition

Let $S$ be a $k$-simplex for some $k \in \Z_{>0}$: $S = \set {\ds \sum_{i \mathop = 0}^k \theta_i \alpha_i}$

A vertex of $S$ is one of the $k + 1$ points $\alpha_0, \alpha_1 \ldots, \alpha_k$.

Also see

• Results about simplices can be found here.

Linguistic Note

The plural of vertex is vertices.

The word vertex is Latin for peak, from which the irregular plural form.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): combinatorial topology
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): combinatorial topology