TITLE: A simplicial complex which is not collapsible, but whose barycentric subdivision is
QUESTION [19 upvotes]: Does anyone know of a simplicial complex which is not collapsible but whose barycentric subdivision is?
Every collapsible complex is necessarily contractible, and subdivision preserves the topological structure, so we are certainly looking for a complex which is contractible, but not collapsible. The only complexes I know of which are contractible but not collapsible are the dunce cap and Bing's house with two rooms. Neither of these have any free faces, and so no iterated subdivision will result in a collapsible complex.

REPLY [10 votes]: @Andy: there is now a small explicit example available, with 15 vertices and 55 tetrahedra, in case you're still interested: it's the 3-ball called $B_{15,66}$ in here. (Sorry for the huge delay and the shameless self-promotion.)