Threecusp

Threecusp is a term used to describe objects, curves, or structures that possess three cusps or pointed projections. It is employed across disciplines as a descriptive label rather than a fixed technical name, and its precise meaning depends on the context.

In geometry, three-cusped curves are curves with three cusp singularities. The most famous example is the deltoid, or three-cusped hypocycloid, formed when a circle rolls inside a larger circle with radius three times smaller. A common parametrization for the deltoid is x(t) = (2R/3) cos t + (R/3) cos 2t and y(t) = (2R/3) sin t − (R/3) sin 2t, where R is the radius of the fixed circle. The deltoid has three cusps and D3 symmetry, and it appears in various areas of geometry and kinematics.

In anatomy, the term can refer to the tricuspid valve of the heart, which normally has three leaflets or cusps. The tricuspid valve lies between the right atrium and right ventricle, and its proper function is essential for unidirectional blood flow; diseases affecting the valve can lead to regurgitation or stenosis.

Other uses of the descriptor appear in heraldry, architecture, or art to denote three-pointed or three-lobed shapes. While threecusp is not a formalized term in all fields, it serves as a concise way to convey the characteristic threefold cuspal feature. See also: cusp, deltoid, tricuspid valve.