Design Nomenclature / Form & Geometry

Torus

Also called donut, toroid, ring

The surface swept by a circle revolved about a coplanar axis it does not intersect. Genus one: the canonical closed surface with a single handle. Its outer band has positive Gaussian curvature, its inner band negative, and the top and bottom circles are exactly parabolic — curvature zero, the boundary between the two.

A wireframe torus in isometric view with the two parabolic circles where curvature passes through zero drawn heavy across the mesh and labelled K = 0, dividing the surface into an outer band labelled K > 0 and an inner band labelled K < 0. The count beneath reads V − E + F = 0, so the genus is one.

Origin

Latin torus, a cushion or bolster, and in classical architecture the convex half-round moulding at the base of a column. The mathematics borrowed the moulding's profile and the name with it.

How this term connects

Gaussian curvatureGenusPrimitiveSweepTopologyTorus
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