DELTOID 3D print model

In geometry, a deltoid curve, also known as a tricuspoid curve or Steiner curve, is a hypocycloid of three cusps. In other words, it is the roulette created by a point on the circumference of a circle as it rolls without slipping along the inside of a circle with three or one-and-a-half times its radius. It is named after the capital Greek letter delta (Δ) which it resembles.

More broadly, a deltoid can refer to any closed figure with three vertices connected by curves that are concave to the exterior, making the interior points a non-convex set.

Ordinary cycloids were studied by Galileo Galilei and Marin Mersenne as early as 1599 but cycloidal curves were first conceived by Ole Rømer in 1674 while studying the best form for gear teeth. Leonhard Euler claims first consideration of the actual deltoid in 1745 in connection with an optical problem.