In geometry, a doughnut-shaped surface is called a torus.
A torus is formed by rotating a circle around an axis in the same plane as the circle but not intersecting it. The familiar ring-shaped torus resembles a doughnut, which is why “doughnut shape” is a common informal description.
A torus has a single continuous hole. In topology, it is often represented as the surface of a square whose opposite edges are identified. This makes it a standard example in the study of surfaces and fundamental groups.
A torus is different from a solid doughnut-shaped object in a technical sense: the mathematical torus usually refers to the surface, while the solid region enclosed by that surface is called a solid torus. The word comes from Latin for a swelling or cushion-like form.