Definition:Face of Simplex

Definition

Let $\sigma$ be a $k$-simplex.

Let $\sigma_k$ denote the set of $k + 1$ vertices of $\sigma$.

Let $r \in \Z_{>0}$ such that $r < k$.

A face of $\sigma$ is an $r$-simplex consisting of a subset of $r + 1$ elements of $\sigma_k$ .

Also see

• Results about simplices can be found here.

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