The 5 Platonic Solids
Only the first 4 Platonic solids were taught publicly by Plato...
One had to be an initiate in his school in order to be introduced to the highest form, the dodecahedron...
One had to be an initiate in his school in order to be introduced to the highest form, the dodecahedron...
Tetrahedron4 vertices (symmetry 3)
4 faces (symmetry 3) 6 edges (symmetry 2) |
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Cube8 vertices (symmetry 3)
6 faces (symmetry 4) 12 edges (symmetry 2) |
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Octahedron6 vertices (symmetry 4)
8 faces (symmetry 3) 12 edges (symmetry 2) |
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Icosahedron12 vertices (symmetry 5)
20 faces (symmetry 3) 30 edges (symmetry 2) |
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Dodecahedron20 vertices (symmetry 3)
12 faces (symmetry 5) 30 edges (symmetry 2) |
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Duals
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Each Platonic solid has a dual...
In the case of the tetrahedron, it is its own dual...
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Nested Platonic SolidsJohannes Kepler modeled the solar system as a nested set of the Platonic solids that predicted the relative orbital diameters of the planets...
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Together with the Quantum Hall Effect, Kepler's work inspired Professor Robert Moon of the Manhattan Project to develop the Moon Model of the nucleus after the nested Platonic solids as well...
This model provides unique insight into the workings of the atomic nucleus, including the propensity of Uranium to fission, since in this model it is a barbell shaped nucleus composed of two dodecahedra attached at one face... |
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Archimedean Solids
The Archimedean Solids have multiple face shapes, but each vertex has identical symmetry, and each edge has identical length...
The 13 Archimedean Solids represent intermediate stages of symmetry development in the filling of nuclear and electron orbital shells...
The Archimedeon Solids, shown below, are listed here with their volumes relative to edge length and their symmetry group(s)...
The 13 Archimedean Solids represent intermediate stages of symmetry development in the filling of nuclear and electron orbital shells...
The Archimedeon Solids, shown below, are listed here with their volumes relative to edge length and their symmetry group(s)...
- 2.7 Truncated Tetrahedron (tetrahedral symmetry)
- 2.4 Cuboctahedron (tetrahedral and octahedral symmetry)
- 13.6 Truncated Cube (octahedral symmetry)
- 11.3 Truncated Octahedron (tetrahedral and octahedral symmetry)
- 8.7 Rhombicuboctahedron (octahedral symmetry)
- 41.8 Truncated Cuboctahedron (octahedral symmetry)
- 7. 9 Snub Cube (octahedral symmetry)
- 13.8 Icosidodecahedron (icosahedral symmetry)
- 85 Truncated Dodecahedron (icosahedral symmetry)
- 55.3 Truncated Icosahedron (icosahedral symmetry)
- 41.6 Rhombicosidodecahedron (icosahedral symmetry)
- 206.8 Truncated Icosidodecahedron (icosahedral symmetry)
- 37.6 Snub Dodecahedron (icosahedral symmetry)
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Catalan Solids
The Catalan Solids are the duals of the Archimedean Solids...
That means the Catalan Solids are defined by connecting vertices located at the face centers of the corresponding Archimedean Solids...
That means the Catalan Solids are defined by connecting vertices located at the face centers of the corresponding Archimedean Solids...
- Triakis Tetrahedron (dual of Truncated Tetrahedron)
- Rhombic Dodecahedron (dual of Cuboctahedron)
- Triakis Octahedron (dual of Truncated Cube)
- Tetrakis Hexahedron (dual of Truncated Octahedron)
- Deltoidal Icositetrahedron (dual of Rhombicuboctahedron)
- Disdyakis Dodecahedron (dual of Truncated Cuboctahedron)
- Pentagonal Icositetrahedron (dual of Snub Cube)
- Rhombic Triacontahedron (dual of Icosidodecahedron)
- Triakis Icosahedron (dual of Truncated Dodecahedron)
- Pentakis Dodecahedron (dual of Truncated Icosahedron)
- Deltoidal Hexecontahedron (dual of Rhombicosidodecahedron)
- Disdyakis Triacontahedron (dual of Truncated Icosidodecahedron)
- Pentagonal Hexecontahedron (dual of Snub Dodecahedron)
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Clinical Theory of Everything
In our model, these Platonic, Archimedean and Catalan solids represent the most fundamental resonance patterns in a spheroidal coherence zone such as a proton, an atomic nucleus, an atom's orbitals, or larger scale entities such as the resonance field of the spirit body's head around the human skull and brain, a comet, a planet, a star, a galaxy, a galactic cluster or the Dark Energy cells that occupy most of the space of the universe...
We look to these geometries and their functional application in 3 dimensional space to seek clues about the nature of both symmetric spatial functions, like gravity, as well as chiral and orthogonal relationships like motion, electricity and magnetism...
We acknowledge that everything has spin, and the spin function affects everything, including gravitation...
Therefore, spin symmetries and stable spin axes are an important factor to consider with these geometries...
With multiple nuclear shells in an atom, and macroscopic shells or their fractal equivalent in an extended vessel, counter-rotation may be a key consideration in producing effects such as levitation in a gravitational field as well as the range of macroscopic expression of quantum effects such as superconductivity and superfluidity that we model as the underlying physiology of natural spiritual functions such as bilocation, subtlety, and the union of previously separate timelines that we call miracles...
For more detail on application of these fundamental geometric considerations to understanding of the personalities of the minerals which make up our bodies, see our update on the Moon Model of the atomic nucleus...
We look to these geometries and their functional application in 3 dimensional space to seek clues about the nature of both symmetric spatial functions, like gravity, as well as chiral and orthogonal relationships like motion, electricity and magnetism...
We acknowledge that everything has spin, and the spin function affects everything, including gravitation...
Therefore, spin symmetries and stable spin axes are an important factor to consider with these geometries...
With multiple nuclear shells in an atom, and macroscopic shells or their fractal equivalent in an extended vessel, counter-rotation may be a key consideration in producing effects such as levitation in a gravitational field as well as the range of macroscopic expression of quantum effects such as superconductivity and superfluidity that we model as the underlying physiology of natural spiritual functions such as bilocation, subtlety, and the union of previously separate timelines that we call miracles...
For more detail on application of these fundamental geometric considerations to understanding of the personalities of the minerals which make up our bodies, see our update on the Moon Model of the atomic nucleus...