Tetrahedral and spherical representations of the periodic system

Abstract

The s, p, d and f blocks of the elements, as delimited by Charles Janet in 1928, can be represented as parallel slices of a regular tetrahedron. They also fit neatly on to the surface of a sphere. The reasons for this are discussed and the possible objections examined. An attempt is made to see whether there are philosophical implications of this unexpected geometrical regularity. A new tetrahedral design in transparent plastic is presented. Keywords Periodic system Á Electronic structure Á Status of helium Plato, in his dialogue Timaeus, supposed that the atoms of the four elements were in the form of four of the regular polyhedra, while the fifth-the dodecahedron-'was used in the delineation of the inhabited world'. After the initial shock of learning that there are at least 120 existing or possible elements, he might have been pleased to know that they can be represented as four parallel and equally spaced slices of a regular tetrahedron. This has been demonstrated by Valery Tsimmerman, an American engineer, Fig. 1. The tetrahedral symmetry had also been noticed by Jess Tauber in 1979 (personal communication) and 2000. Tsimmerman's starting point was the blocks of chemical elements as delimited by Janet (1928), a French engineer and amateur biologist and geologist, who turned his mind to the Periodic System at the age of 78. Janet arrived at his 'left-step table' by moving what is now called the s block from the left-hand side of the long form of the table to the right-hand side, placing H and He at its head and making Li and Be into the second period. In consequence his periods are different from those in other tables; B to Mg are pushed down into the third period, and there are in all eight periods. There is no reason to object to this; the delimitation of periods is arbitrary; the Greek periodos means simply 'coming around'.