Moderate Degree Symmetric Quadrature Rules for the Triangle

A variant formulation of the moment fitting equations for the construction of D3 (triangularly symmetric) quadrature rules for the triangle is derived. These equations are solved to produce weights and abscissas for quadrature rules of polynomial degree up to 11 for the triangle, some of which require fewer function evaluations than any presently available rule of the same polynomial degree. Cytolic rules of degrees up to 9 are also derived.