From teaching experience. XIV. On the variety of tetrahedrons

Abstract

The paper proposes the derivation of 25 combinatorial-geometric kinds of tetrahedrons belonging to 8 point symmetry groups. Among them are 3 simple forms: cubic (-43m), tetragonal (-42m) and rhombic (222) tetrahedrons; and 5 combinations: trigonal pyramid and monohedron (3m), 2 planar dihedrons (mm2, 2 kinds), 2 axial dihedrons (2, 3 kinds), planar dihedron and 2 monohedrons (m, 5 kinds), 4 monohedrons (1, 11 kinds). It is shown that tetrahedrons with symmetry 23, -4 and 3 — subgroups of the point symmetry group of the cubic tetrahedron — are impossible. The example is recommended for consideration in the course of crystallography on «simple forms and their combinations».