geomety

Divining with the Five Platonic Solids.

Named after the philosopher Plato, though dating thousands of years before his time, the five Platonic solids illuminate the five elements and their clashing yet complementary chemistry. When viewed allegorically, Plato’s Solids suggest a unifying mission that ultimately unites us with the One. According to Plato, the four elements individually illuminate a singular aspect of itself to the other, while the fifth element, seen as the Cosmos, unifies and embodies the four. This elemental alliance allows the fifth element to express itself as the greater whole, or as some say, the Divine plan. Seen this way, the Solids reveal a dance that moves in unison with the Cosmos. This dance can be viewed as a guiding principle that lends itself to the Understanding of our greater mission and through Divination we can co-create the dance of the many to illuminate our Spirit’s Connection with the One.

The goal of this illustration is to let the five Platonic solids lead the way to what matters by contemplating on each element and their corresponding statement. Each statement invites reflection and bypasses the typical everyday focus. This is not about our love life, career or income. Instead it’s about promoting answers from a deeper perspective. 

Moses Harris - Prismatic Colors, “The Natural System of Colors”, 1766.

Moses Harris’s chart was the first full-color circle. The 18 colors of his wheel were derived from what he then called the three ‘primitive’ colors: red, yellow and blue. At the center of the wheel, Harris showed that black is formed by the superimposition of these colors. Mimicking the spread of light from a source, Harris places the pure colors at the center of his circle and the lightest at the outer edge.

The Melancholy Solid

The exact geometry of the solid depicted by Albrecht Dürer in Melencolia I, is subject of a vivid academic debate. According to Terence Lynch (1982), the hypothesis that the shape is a misdrawn truncated cube was promoted by Walter L. Strauss in 1972. 

However most sources agree that it is the truncation of a rhombohedron. David H. Richer (1957) claims in his famous Perspektive und Proportionen in Albrecht Dürers ‘Melancholie’, that the rhombi of the rhombohedron from which this shape is formed have 5:6 as the ratio between their short and long diagonals. Thus the acute angles of the rhombi would be approximately 80°.

After much reflection, Eberhard Schröder (1980) and Terence Lynch (1982) instead concluded that the ratio is √3:2 and the angle approximately 82°.

In 1981 Carolina H. Mac Gillavry entered public controversy in the Netherlands, claiming that the acute angle is approximately 79°. She discovered this by measuring two lengths on the engraving that are not distorted by perspective.

Peter Schreiber argues in 1999, based on the writings of Dürer that all vertices of Dürer’s solid lie on a common sphere, and further claims that the rhombus angles are 72°.

In 2004 Hans Weitzel analyzes a 1510 sketch by Dürer of the same solid, from which he confirms Schrieber’s hypothesis that the shape has a circumsphere but with rhombus angles of approximately 79.5°. The two men frequently corresponded after this.

Further reading: http://tiny.cc/4uk7mx

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