  We obtain a geometric realization of a minimal 8-vertex triangulation of the
dunce hat in Euclidean 3-space. We show there is a simplicial 3-ball with 8
vertices that is collapsible, but also collapses onto the dunce hat, which is
not collapsible. This 3-ball is as small as possible, because all triangulated
3-balls with fewer vertices are extendably collapsible. As we will see, the
Alexander dual of the dunce hat is collapsible.
