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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 ...
The Theory of Forms or Theory of Ideas, [1] [2] [3] also known as Platonic idealism or Platonic realism, is a philosophical theory widely credited to the Classical Greek philosopher Plato. A major concept in metaphysics , the theory suggests that the physical world is not as real or true as Forms.
In Middle Platonism, the Platonic Forms were not transcendent but immanent to rational minds, and the physical world was a living, ensouled being, the World-Soul. Pre-eminence in this period belongs to Plutarch .
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]
Unlike the case of the other Platonic solids, all the vertices of a regular tetrahedron are equidistant from each other (they are the only possible arrangement of four equidistant points in 3-dimensional space, for an example in electromagnetism cf. Thomson problem). The above embedding divides the cube into five tetrahedra, one of which is ...
There are 5 finite convex regular polyhedra (the Platonic solids), and four regular star polyhedra (the Kepler–Poinsot polyhedra), making nine regular polyhedra in all. In addition, there are five regular compounds of the regular polyhedra.
Plato's theory of the soul, which was inspired variously by the teachings of Socrates, considered the psyche (Ancient Greek: ψῡχή, romanized: psūkhḗ) to be the essence of a person, being that which decides how people behave. Plato considered this essence to be an incorporeal, eternal occupant of a person's being.