We introduce the concepts of spherical deltoid of type II and spherical deltoid of type II, describing geometrical methods to construct both types. It is shown that any spherical deltoid is congruent to a spherical deltoid of type I and to a spherical deltoid of type II. We classify spherical deltoids taking into account the relative positions of the spherical moons containing their sides. This allows us to conclude that the class of all spherical deltoids is a differentiable manifold of dimension three.

CEMAT - Center for Computational and Stochastic Mathematics