Sacred Geometry: Golden Ratio in Platonic Solids

The golden mean, or larger segment AC, is in the same ratio to the mean ratio as the mean ratio is to the whole, that is, the sum of the two segments AB. The three elements involved, while remaining hierarchically distinct and with their hierarchical structure determined by the different dimensions of the segments, all live by a single ratio that is transmitted from the larger segment to the smaller one or from the smaller to the larger, thus forming an indivisible unitotality. The golden ratio transmission model has been identified, since Kepler's time, as a model of communion and transmission, typical of ideal and unitotal creation. In it every created being, however small, is united to the heart of divine light. "I believe that this geometric proportion served the Creator when he introduced the creation of likeness from likeness, which continues indefinitely" - Kepler. In the spiritual realm, perfect transmission, according to a pre-established hierarchical structure, is realized through that interior movement of love in which the individual transcends himself by overcoming egoism, in a surge of self-overcoming that constitutes sacrifice. By doing so, overcoming his individual limits rooted in his own egoism, the individual opens himself to divine influence and becomes permeated with the idea of divine unity. The end of this process is a total spiritual reintegration, which, in a certain sense, represents the very end of universal evolution: the fulfillment of all Creation through the assumption of the Uncreated Principle. The complete and perfect materialization of divinity corresponds to the perfect incarnation of the Idea of God in Creation, that is, to supreme beauty, whose geometric symbol is precisely the golden ratio or golden number. By dividing the 12 sides of the Octahedron in golden ratio, we obtain the vertices of the Icosahedron, which have coordinates $\{(0;\varphi;1);(1;0;\varphi);(\varphi;1;0)\}$, where we have used the previously stated convention that $\varphi = 1.618...$. Each of these 12 vertices brings together 5 equilateral triangles. The Number 5 therefore appears naturally in the Icosahedron and, consequently, in the Dodecahedron which is its dual solid. The Icosahedron has been considered a symbol of Individuality, where the individual triangular faces represent the individual Personalities. Personality is that part of Individuality that manifests in a given time, in a given reincarnation, in a given particular race, now as man, now as woman. Conversely, Individuality is the immortal Soul of Man that resists physical death and can manifest in a physical body only in part. From the Icosahedron, through the duality operation, we obtain the Dodecahedron whose sides are in golden ratio to those of the original Icosahedron. This means, in other words, that if we suppose to proceed by duality starting from an icosahedron of side 1, we will obtain a dodecahedron of side $\varphi^{-1} = 0.618...$ having as center of faces the vertices of the original icosahedron. The Dodecahedron in the series of five regular polyhedra that spring one after another from numbers, expresses the most perfect synthesis of the universe. The Dodecahedron has a powerful magical power. For symbolism the 12 faces recall the twelve Signs of the Zodiac; this symbol points to the Universe and is a Pythagorean symbol. It has reference to the Heavenly Jerusalem. It recalls the Apocalypse of John ch.21,23. It also recalls for the "New Jerusalem" the 12 gates, the 12 Angels, the walls of 12 foundations, the 12,000 stadia on each side. The word of power is the Hebrew Alleluia which means: "The Lord be praised". The Dodecahedron is a universal symbol, in which the Pentagram, symbol of Spirit and Light, is modulated by the Number 12, number of the perfect cycle, of perfect redemption and intelligence of Light. If transparent and illuminated from within, the Dodecahedron is a perfect symbol of the Sun acting on Earth and on men through 12 faces or faces expressed by the 12 Signs of the Zodiac. More precisely, the Dodecahedron contains all the Numbers that regulate the rhythms of terrestrial evolution under the influence of the Sun. The 12 faces refer to the 12 Signs of the Zodiac that divide the year or solar cycle; the 30 edges of the polyhedron refer to the 30 degrees, corresponding to 30 days, into which each zodiacal Sign is divided and, finally, the 20 vertices refer to the 20 divisions of the day, each equal to 72 minutes. In the Dodecahedron we thus find the progressive division of the solar cycle: $12 \text{ signs} \times 30 \text{ degrees} \times 20 \text{ divisions} \times 72 \text{ minutes}$. From these divisions, by analogy and correspondence, others derive that determine the terrestrial cycles and the Eras of Humanity's development. The Dodecahedron is a regular polyhedron and, therefore, is the expression of a perfection achieved. It is a synthetic symbol of universal perfection, of the completion of the organic evolution of all Creation. The purpose of all creation is the assumption of the uncreated transfiguring principle.