# Hatcher 2.1.24

Hatcher, Algebraic Topology, Chapter 2, Section 1

24. Show that each $n$-simplex in the barycentric subdivision of $\Delta^n$ is defined by $n$ inequalities $t_{i_0}\leq t_{i_1}\leq\cdots\leq t_{i_n}$ in its barycentric coordinates, where $(i_0,\ldots,i_n)$ is a permutation of $(0,\ldots,n)$.
Proof.

$\square$