[size=85]Let the vertices of the initial polyhedron belong to the same sphere. On its basis, can be constructed a certain series of polyhedra. The vertices of each of them are the points of the trisections of the segments of the original polyhedron that have the same length (calculated with a certain accuracy). Obviously, the number of vertices of the constructed polyhedron is twice the number of trisected segments and they all lie on the same sphere. Let [b]g[/b] be the ordinal number of the various segments of the initial polyhedron.[br]Geometric Constructions are in [url=https://www.geogebra.org/m/p4a5zccm]Applet[/url]. [/size]