Pinched torus

In mathematics, and especially topology and differential geometry, a pinched torus (or croissant surface) is a kind of two-dimensional surface.

It gets its name from its resemblance to a torus that has been pinched at a single point.

A pinched torus is an example of an orientable, compact 2-dimensional pseudomanifold.

An example of such a parametrisation − which was used to plot the picture − is given by ƒ : [0,2π)2 → R3 where: Topologically, the pinched torus is homotopy equivalent to the wedge of a sphere and a circle.

[2][3] It is homeomorphic to a sphere with two distinct points being identified.