Diangle

The diangle ABCD indicates the entire duration of life, A and C being its commencement and its termination.

Now the wedge 1,2 is mapped into the exterior of the circular diangle C,S₁,1,O,2,S₂,C; both regions are indicated by a shading of the boundary. We now seek the images of the reflected wedges.

Let B be a region of F bounded by a closed polygon comprised of segments of geodesics of surface F, and let hₙ be a sequence of nondegenerate diangles of region B whose sides are geodesics of region B and which converge to diangle hₙ.