How the Nucleus Grows
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Building atoms one sphere at a time,
Edo discovered that there are a limited number of possibilities for how spheres can be put together.
 One sphere can exist in one way, by itself. A single sphere incorporates all dimensions and shapes within itself.
 Two spheres can stick together in only one way, next to each other. This gives direction and depicts one dimension.
 With three spheres there are two possibilities, all in a line which is one dimension or in the shape of a triangle which is two dimensions .

Four spheres have three possibilities  all four in a line (one dimension), in the shape of a square (2 dimensions) and in the shape of the tetrahedron (3 dimensions). Four in a line doesn't work, this would be Quatrium, a new isotope of hydrogen. The square is not densely packed which is a primary rule. This leaves the tetrahedron, the first shape that is 3dimensional. It is densely packed and quite stable as it cannot be easily crushed or distorted. It is the simplest of the platonic solids.Helium 4
 You cannot add a fifth proton without distorting the structure of the tetrahedron. The inward pulling force pulls breaks it: there is no stable structure with 5 spheres and hence there is no element with 5 nucleons. The spheres push each other out of a dense structure and create distortions in the shape. There is no final resting shape for clusters of five spheres.
 Six spheres create an octahedron and at first glance this appears to be stable and densely packed. However, since the spheres are being pulled toward a common center, opposite spheres will push apart the 4 connected protons and instead create a 5 sphere ring structure with an additional sphere on one side at the center of the ring. This structure is lithium 6. However it is imbalanced and Lithium 6 is only 7.5% of the natural occuring lithium.

Seven spheres complete a pentagonal bipyramid or Lithium 7. This shape has 10 triangular faces and many of the attributes of a platonic solid. The pentagonal bipyramid can be thought of as a partial icosahedron. You can build an icosahedron with magnets by creating two rings of five, putting them together into a cylinder of two interlocking rings, then adding one more magnet to each end. The pentagonal bipyramid is the same shape minus one of the two rings of 5.
Lithium is the first shape that creates a ring of 5 spheres. This ring gives lithium its valence of 1. Lithium is also the first element that creates solid matter.
Edo intuitively realized the pentagonal bipyramid (lithium) is a most interesting and profound shape. This understanding was key to his correlating densely packed spherical structures with the Periodic Table. This realization changed his focus from playing with shapes spheres can make to developing SAM  The nucleus of the atom has a structure based on geometrical spherical dense packing, and this structure determines the properties of the elements.  Eight spheres create the same conditions found with 5 spheres. The inward pulling force causes the 8th sphere to penetrate the ring below it and break the underlying structure. You cannot get a stable structure that is densely packed with 8 spheres. Therefore there are no stable elements with 8 nucleons.
 Nine  When adding two spheres together you create a tetrahedron that combine with two spheres already in the structure. This tetrahedron is stronger than the underlying structure and modifies it accordingly, therefore the underlying structure is not destroyed as it was when adding the eighth sphere. This is Beryllium 9.
 Adding a 10th sphere creates Boron 10. It has 3 interlocking rings of five which give it a valence of 3. However this structure is incomplete and only 20% of the naturally occurring boron is boron 10.
 The 11th sphere completes the structure and creates Boron 11 which is 80% in abundance. There are 4 interlocking rings of 5 but by observation only 3 can have an active rotation without causing opposition in the rings.

Adding a 12th sphere creates the element Carbon in the shape of the Icosahedron, the largest platonic solid that can be densely packed. The Icosadhedron has 20 faces each being an equilateral triangle with 3 protons at the vertices. This is a very stable structure and is the building block of the larger atoms. Even though it follows the rules for spherical dense packing toward a common center, it is hollow on the inside.Carbon 12
Generally speaking, adding two spheres creates the next ring and therefore the next element until a complete icosahedron is created, However there are exceptions to this rule, and SAM explains those exceptions which is explained in more detail later.