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 [1], 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.

[1] Zeeman, E. C. (1964). "On the dunce hat". Topology. 2 (4)