Series of polyhedra obtained by trisection (truncation) segments of the original polyhedron

Geometric Constructions. 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 g be the ordinal number of segments of the initial polyhedron that have the same length. With this applet, you can explore trisections for multiple polyhedra by clicking the corresponding button. Their captions contain information about the average length of the segments of each of them inscribed in a sphere of unit radius. Images are in Applet.