Cone ranks and a simple way to recognize these ranks

Abstract

If, taking the center of the cone as the center of the sphere, we intersect it with the surface of this sphere, then the cone will be replaced by a spherical coneprime, which is why the task at hand is reduced to recognizing the ranks of coneprime on the sphere. A similar problem of determining the ranks of flat conoprimes is resolved by determining the type of involution of the points of the conoprime on an extra straight line (infinitely distant) or the involution of rays at its center. The article introduces new ranks of conoprimes and a method for recognizing them.