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The Platonic solids have been known since antiquity. It has been suggested that certain carved stone balls created by the late Neolithic people of Scotland represent these shapes; however, these balls have rounded knobs rather than being polyhedral, the numbers of knobs frequently differed from the numbers of vertices of the Platonic solids, there is no ball whose knobs match the 20 vertices ...
According to Stephen Skinner, the study of sacred geometry has its roots in the study of nature, and the mathematical principles at work therein. [5] Many forms observed in nature can be related to geometry; for example, the chambered nautilus grows at a constant rate and so its shell forms a logarithmic spiral to accommodate that growth without changing shape.
In philosophy and specifically metaphysics, the theory of Forms, theory of Ideas, [1] [2] [3] Platonic idealism, or Platonic realism is a theory widely credited to the Classical Greek philosopher Plato. The theory suggests that the physical world is not as real or true as "Forms".
The convex regular dodecahedron is one of the five regular Platonic solids and can be represented by its Schläfli symbol {5, 3}. The dual polyhedron is the regular icosahedron {3, 5}, having five equilateral triangles around each vertex.
The five Platonic solids have an Euler characteristic of 2. This simply reflects that the surface is a topological 2-sphere, and so is also true, for example, of any polyhedron which is star-shaped with respect to some interior point.
The 5 Platonic solids are called a tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron with 4, 6, 8, 12, and 20 sides respectively. The regular hexahedron is a cube . Table of polyhedra
The fifth element (i.e. Platonic solid) was the dodecahedron, whose faces are not triangular, and which was taken to represent the shape of the Universe as a whole, possibly because of all the elements it most approximates a sphere, which Timaeus has already noted was the shape into which God had formed the Universe. [9]
The regular tetrahedron is also one of the five regular Platonic solids, a set of polyhedrons in which all of their faces are regular polygons. [4] Known since antiquity, the Platonic solid is named after the Greek philosopher Plato , who associated those four solids with nature.