Geometric Model by A. Harry Wheeler, Supplementary Trihedral Angles

Three planes that meet at the center of a sphere form what is called a trihedral (three-sided) angle. Each plane intersects the sphere in a great circle. Segments of these three circles form a spherical triangle on the sphere. In this cut and folded tan paper model, Wheeler labels the vertices of this triangle ABC. Consider a point (not named by Wheeler – call it X) inside the bounds of the trihedral angle and drop perpendiculars to the three sides of the trihedral angle through it. Wheeler calls the points of intersection D, E, and F. The trihedral angle centered at X is the supplement of the original trihedral angle.