The most symmetrical and efficient 3-dimensional shape is the tetrahedron. This is the first platonic solid. This lightest, least complex, most prevalent element is Hydrogen; single proton / electron pair. The next pairing is Helium. These two protons are bound together, and the electrons repelling each other. Their attempt to get as much distance between them results in a 180-degree separation. Next is Lithium with three pairs. Now the distance between the vortex tubes is reduced to 120-degree separation (in 3-dimensions). The fourth element, Beryllium, has now reached a level of maximum symmetry. Imagine both your arms and legs spread out equidistant from each other; this is a tetrahedron.

All four elements just mentioned have a 90-degree based crystal structure. This implies some level of symmetry. The fifth element, Boron, is the first oblique (non 90-degree) crystal structure. Boron is also, at this point, the most asymmetrical position in the platonics. On the way to the next level of perfect symmetry, to the eight element, is Oxygen. This takes the form of a dual-paired tetrahedron; this is the first resonance chamber.

The tetrahedron has four vertices and four faces. It is either the vertices, or the faces (not both) that represent the proton – vortex tube locations in the platonic configuration. For simplicity, let’s just focus on the vertices. Imagine the four proton/electron pairings of Beryllium. There is a miniature tetrahedron configuration of the four protons, each proton residing at the vertex of the tetrahedron. In exact geometric symmetry extending out from this inner tetrahedron of protons is a larger tetrahedron representing the vortex tubes. Essentially there is a smaller tetrahedron surrounded by a larger one. This is Beryllium.

The next four elements, from Boron to Oxygen, duplicate this process. The first complete shell ends up being the dual-paired tetrahedron, having a total of eight vertices. This is a point of maximum symmetry, the key being both the faces and vertices equal each other. There is no other configuration able to add to this symmetry. The next proton/electron pairing entering into existence, Fluorine as the 9th element, naturally extends out to form the 2nd shell.

At this point in the progression, this 9th element, which is also the 1st element beyond the symmetrical dual-paired tetrahedron, the 1st element of the 2nd shell, is at the most asymmetrical position. Fluorine is the 2nd element to have an oblique crystal structure. At this point in the development, that leaves us with 2 positions of maximum asymmetry: position 5 and position 9.

Element Platonic Position in platonic Symmetrical Crystal Structure
Hydrogen tetrahedron 1:4 Yes 90
Helium tetrahedron 2:4 Yes 90
Lithium tetrahedron 3:4 Yes 90
Beryllium tetrahedron 4:4 Yes 90
Boron d/p tetrahedron 5:8 No Non-90
Carbon d/p tetrahedron 6:8 Yes 90
Nitrogen d/p tetrahedron 7:8 Yes 90
Oxygen d/p tetrahedron 8:8 Yes 90
Fluorine cube 1:6 No Non-90
Neon cube 2:6 Yes 90
Sodium cube 3:6 Yes 90
Magnesium cube 4:6 Yes 90
Aluminum cube 5:6 Yes 90
Silicon cube 6:6 Yes 90
Phosphorous d/p cube/octahedron 1:14 No Non-90


RC # Platonic Solid # of V # of F R of D Actual Min Max
1 d/p tetrahedron 8 8 0 8 8 8
2 cube 8 6 2 6 6 8
3 d/p cube / octahedron 14 14 4 9 12 16
4 dodecahedron 20 12 8 6 12 20
5 d/p dodecahedron / icosahedron 32 32 16 11 24 40
6 d/p tetrahedron 8 8 0 8 8 8
7 cube 8 6 2 7 6 8
8 d/p cube / octahedron 14 14 4 11 12 16
9 dodecahedron 20 12 8 7(+1) 12 20
10 d/p dodecahedron / icosahedron 32 32 16 10 24 40
11 d/p tetrahedron 8 8 0 8(+2) 8 8
12 icosahedron 12 20 8 20(+3) 12 20

Note: this is an explanation of the column names from the table below.

Col #1 – RC # = Resonance Chamber number.

Col #2 – Platonic Solid = the Platonic Solid. d/p = Dual Paired.

Col #3 – Number of Vertices = total number of vertices available, including dual pairing.

Col #4 – Number of Faces = total number of faces available, including dual pairing.

Col #5 – Range of Difference = the difference between highest and lowest number of available vertices and faces.

Col #6 – Actual = the actual number of elements on the Ajax Model for given row number. The ‘(+n)’ signifies number of shared nodes.

Col #7 – Minimum = the minimum number of vertices and/or faces available based on platonic solid construct.

Col #8 – Maximum = the maximum number of vertices and/or faces available based on platonic solid construct.


Each of the shells resonates to a continually changing or pulsating combination of Solfeggio frequencies. There is not a fixed, static frequency per se, but a form of atomic fractal pattern induction. Each resonance chamber is represented by a Solfeggio symbol. Each symbol represents a unique combination of varying ratios or multiples of 3, 6 and 9 with Solfeggio at its root.