The Symmetry System
About the author
Symmetry symbols
Electrical axes
Orbital polyhedron
Syn-epi switch
Accretion of structure
Symmetry of atoms
Accretion of atoms



Orbital polyhedron

The symmetrical spatial configuration of all electrical axes belonging to a particular symmetry defines its orbital polyhedron. Fig. 3g shows the orbital polyhedron of the non-polar 6фO symmetry. It comprises 12 negative and 12 positive non-polar axes. Fig. 3h represents the orbital polyhedron of the polar 4χN symmetry as a spatial combination of four spatially equal polar electrical axes.

Figure 3

  a b
Figure 03a Figure 03b

c d e f
Figure 03c Figure 03d Figure 03e Figure 03f

g h
Figure 03g Figure 03h

The symmetric parameter that gives the relationship between the nodal point and the starting point of the Cartesian co-ordinations system, for which x = y = z = 0 holds true, is a centricity. The nodal point of a particular symmetry can be identical with this point. However, it can be placed at some specific positions or elsewhere. See the Table 2 for exact definitions.

Fig. 4 gives some further examples of orbital polyhedrons. The positions of x = y = z = 0 points are marked by the crossed circles in order to show the centricity of non-centric symmetries.

Table 3 lists all symmetries in accordance with the number of non-polar or polar electrical axes comprising each particular orbital polyhedron. The lower is the number of electrical axes, the more polar is a particular symmetry, regardless of its non-polar or polar character.

If we increase the number of electrical axes towards the infinity then three different situations evolve. In acentric symmetries belonging to H and T we obtain the orbital polyhedron consisting of an infinite number of electrical axes that are packed so closely that they melt into a single polar electrical axis of the highest symmetry Χ. See Figs. 3e and 3f.

In all centric symmetries except for ω ones the infinite number of electrical axes (non-polar or polar) melt together and form a single non-polar electrical axis of the highest symmetry Φ circumvented by an oppositely charged torus. Imagine the same situation as on the Fig. 3g but with the infinite n.

The infinite increase in the number of non-polar or polar electrical axes in all ω-type symmetries ends in the highest symmetry Ω. The axes are so tightly packed that we cannot differentiate between their charges any more. An electro-neutral sphere results.

If we consider the charges of the highest symmetries then we can conclude that the symmetry Χ is a polar one and the symmetry Ω an electro-neutral one. The situation with the non-polar Φ symmetry is different. Two configurations are possible. The first has a positive torus and negative lobes. The second is similar, yet the charges of its torus and lobes are reversed and consequently the configuration of the orbital polyhedron, too. The first has a leptoidal (spindle-shaped), whereas the second a pithoidal (barrel-shaped) morphology. Fig. 3g, shows the leptoidal situation. The spatial reversal of all electrical axes results in the pithoidal configuration.

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