Constructing Fully Symmetriccubature Formulae for The

We construct symmetric cubature formulae of degrees in the 13-39 range for the surface measure on the unit sphere. We exploit a recently published correspondence between cubature formulae on the sphere and on the triangle. Speciically, a fully symmetric cubature formula for the surface measure on the unit sphere corresponds to a symmetric cubature formula for the triangle with weight function (u 1 u 2 u 3) ?1=2 , where u 1 , u 2 , and u 3 are homogeneous coordinates.