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The Five Platonic Solids
Polyhedra whose faces are all regular polygons with the same number of corners are called "regular polyhedra." The five Platonic solids are the five, convex, regular polyhedra that can exist in 3-dimensional space. Each Platonic solid appears in Nature in some way. The tetrahedron, octahedron & cube all occur as crystals. For example, salt crystals are cubic, fluorite (calcium fluoride, CaF_{2}) are octahedral. The icosahedron and dodecahedron do not appear in crystal forms, although one, called the pyritohedron, which makes up pyrites ("Fool's Gold," iron sulphide, FeS_{2}) has 12 irregular pentagonal faces. Living organisms also assume the shapes of Platonic solids. The outer protein shells of many viruses form regular polyhedra. For example, the HIV virus is enclosed in a regular icosahedron.
Tetrahedron | Octahedron | Cube | Icosahedron | Dodecahedron | Total | |
Vertices: | 4 | 6 | 8 | 12 | 20 | 50 |
Edges: | 6 | 12 | 12 | 30 | 30 | 90 |
Faces: | 4 | 8 | 6 | 20 | 12 | 50 |
Total: | 14 | 26 | 26 | 62 | 62 | 190 |
The Decad (10) determines the 190 vertices, edges & faces of the five Platonic solids because 190 = 10×19, where 19 is the tenth odd integer. It will be shown later that it determines the number of points, lines & triangles that make up their faces. Each half of the five solids has 95 vertices, edges & faces. The number 95 is the number value of Madim, the Mundane Chakra of Geburah, the fifth Sephirah from the top of the Tree of Life (see table). There are 26 of them in half the octahedron and half the cube and 31 of them in either half the icosahedron or half the dodecahedron. 26 is the number value of YAHWEH, the Godname of Chokmah, and 31 is the number value of EL, the Godname of Chesed, which is the Sephirah below Chokmah on the Pillar of Mercy of the Tree of Life. ELOHIM, the Godname of Binah with number value 50, prescribes the five Platonic solids because they have 50 vertices and 50 faces. They have 140 vertices & edges and 140 edges & faces. 140 is the number value of Malachim, the Order of Angels assigned to Tiphareth. The dodecahedron have 62 vertices, edges & faces, where 62 is the number value of Tzadkiel, the Archangel of Chesed. These representatives of the Sephiroth in the four Kabbalistic Worlds appear not by accident (all the numbers of their other representatives can be shown to characterize the five Platonic solids in various ways) but because the mathematically complete set of five regular polyhedra constitute a holistic system whose properties are measured by the gematria number values of the Hebrew names of the Sephiroth, their Godnames, Archangels, Orders of Angels & Mundane Chakras. What most Kabbalists do not realize is that this set of 50 numbers parameterizes not only the outer and inner Tree of Life but all holistic objects possessing sacred geometry. They have a universal significance that transcends the mystical traditions of any particular religion. These numbers must be regarded as more fundamental than the Hebrew words that act as their vehicles. This is why they manifest in many non-Kabbalistic contexts, e.g., the Platonic solids, as the author's research articles and his latest book amply illustrate.
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