995.11A The sequence is as follows: *(Magic Numbers)*One-frequency tetrahedron: 6 vectors timesA=2 Two-frequency tetrahedron: 24 vectors times A=& Three-frequency tetrahedron: 60 vectors times 1/3 =20 Thr ee frequency tetrahedron + t wo-frequency tetrahedron: 60 vectors + 24 vectors ti mes V3 =28 Four-frequency tetrahedron + one-frequency icosahe d ron: 120 vectors + 30 vectors times V3 =50 Five-frequency tet r ahedron + one-frequency tetra hedron + one-frequency icosahedron: 210 + 6 + 30 ve ctors times V3 =82 Six-frequency tetrahedron + one-frequency oc tahedron + o ne-frequency icosahedron: 336+ 12 + 30 vectors times\sfrac{1}{3} = 126
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Figure 48: Fig. 995.03A Vector Models of Atomic Nuclei: Magic Numbers: In the structure of atomic nuclei there are certain numbers of neutrons and protons which correspond to states of increased stability. These numbers are known as the magic numbers and have the following values: 2, 8, 20, 28, 50, 82, and 126. A vector model is proposed to account for these numbers based on combinations of the three fundamental omnitriangulated structures: the tetrahedron, octahedron, and icosahedron. In this system all vectors have a value of one-third. The magic numbers are accounted for by summing the total number of vectors in each set and multiplying the total by $\sfrac
{1}{3}$. Note that although the tetrahedra are shown as opaque, nevertheless all the internal vectors defined by the isotropic vector matrix are counted in addition to the vectors visible on all the faces of the tetrahedra.Figure 49: Fig. 995.31A Reverse Peaks in Descending Isotope Curve: Magic NumbersFigure 49: Fig. 995.31A Reverse Peaks in Descending Isotope Curve: Magic Numbers
995.12 Magic Number 28: The Magic Number 28, which introduces the cube and the octahedron to the series, was inadvertently omitted from Synergetics 1. The three-frequency tetrahedron is surrounded by an enlarged two-frequency tetrahedron that shows as an outside frame. This is a negative tetrahedron shown in its halo aspect because it is the last case to have no nucleus. The positive and negative tetrahedra combine to provide the eight corner points for the triangulated cube. The outside frame also provides for an octahedron in the middle. (See revised Figs. 995.03A and 995.31A.)
995.20 Counting
995.21 In the illustration, the tetrahedra are shown as opaque. Nevertheless, all the internal vectors defined by the isotropic vector matrix are counted in addition to the vectors visible on the external faces of the tetrahedra.