# Hatcher 2.1.23

Hatcher, Algebraic Topology, Chapter 2, Section 1

23. Show that the second barycentric subdivision of a $\Delta$-complex is a simplicial complex. Namely, show that the first barycentric subdivision produces a $\Delta$-complex with the property that each simplex has all its vertices distinct, then show that for a $\Delta$-complex with this property, barycentric subdivision produces a simplicial complex.
Proof.

$\square$