The dunce hat is a topological space obtained by gluing the three edges of a solid triangle following certain orientations. Due to E. C. Zeeman, it is a classical example of a space that is contractible, but not in an obvious way (it is not collapsible, in particular it has no boundary point where a contraction can start).
This space embeds in \(\mathbb{R}^3\). The animation shows a deformation of the triangle into the dunce hat.