431.00 Volume

431.01 The vector equilibrium consists of six one-half octahedra, each with a volume of two (6 \times 2 = 12), and eight tetrahedra each with a volume of one, so 8 + 12 = 20, which is its exact volume. (See illustration 222.30. )

431.02 The volume of a series of vector equilibria of progressively higher frequencies is always frequency to the third power times 20, or 20F³, where F = frequency. When the vector equilibrium’s frequency is one (or radia- tionally inactive), its volume is 20 \times 1^{3}= 20.

431.03 But frequency, as a word key to a functional concept, never relates to the word one because frequency obviously involves some plurality of events. As a one-frequency, ergo sub-frequency, system, the vector equilibrium is really subsize, or a size-independent, conceptual integrity. Therefore, frequency begins with twowhere all the radials would have two increments. When the edge module of a cube is one, its volume is one; when the edge module of a cube is two, its volume is eight. But when the edge module of a vector equilibrium is one, its volume is 20. A nuclear system is subsize, subfrequency. Equilibrious unity is 20; its minimum frequency state is 160 = 2^{5}\times 5. This is one of the properties of 60-degree coordination.

431.04 Looking at a two-frequency vector equilibrium (with all the radials and edge units divided into two) and considering it as the domain of a point, we find that it has a volume of 480/1 and B Modules. The formula of the third power of the frequency tells us the exact number of quanta in these symmetrical systems, in terms of quantum accounting and in terms of the A and B Modules (see Chapter 9, Modelability).