cross-section of the set of unistochastic matrices of order three forms a deltoid. The set of possible traces of unitary matrices belonging to the group SU(3) forms a deltoid. The intersection of two deltoids parametrizes a family of complex Hadamard matrices of order six. The set of all Simson lines of given triangle, form an envelope in the shape of a deltoid. This is known as the Steiner deltoid or Steiner's hypocycloid after Jakob Steiner who described the shape and symmetry of the curve in 1856. The envelope of the area bisectors of a triangle is a deltoid (in the broader sense defined above) with vertices at the midpoints of the medians. The sides of the deltoid are arcs of hyperbolas that are asymptotic to the triangle's sides. A deltoid was proposed as a solution to the Kakeya needle problem. See also Astroid, a curve with four cusps Circular horn triangle, a three-cusped curve formed from circular arcs Ideal triangle, a three-cusped curve formed from hyperbolic lines Pseudotriangle, a three-pointed region between three tangent convex sets Tusi couple, a two-cusped roulette Kite (geometry), also called a deltoid References "Tricuspoid" at MacTutor's Famous Curves Index "Deltoid" at MathCurve Algebraic curves Roulettes (curve)