# Simplicial subdivision

Given a simplex, $LaTeX: S$, its simplicial subdivision is a collection of simplices, say $LaTeX: \{T_i\}$ such that $LaTeX: \textstyle \lor_i\{T_i\} = S$ and for any $LaTeX: i$ and $LaTeX: j$, either the intersection $LaTeX: \textstyle T_i \land T_j$ is empty or equals the closure of a common face. The mesh of the subdivision is the diameter of the largest sub-simplex. This arises in a fixed point approach to compute an economic equilibrium.