TITLE: Is every finite CW complex is homotopic to simplicial complex?
QUESTION [5 upvotes]: Is every finite CW complex is homotopy equivalent to a simplicial complex?

REPLY [6 votes]: This is theorem 2C.5 p.182 from Hatcher's Algebraic Topology:

Every CW complex X is homotopy equivalent to a simplicial complex,
  which can be chosen to be of the same dimension as X, finite if X is
  finite, and countable if X is countable.