# Platonic solid

Platonic solid
one of the five regular polyhedrons: tetrahedron, octahedron, hexahedron, icosahedron, or dodecahedron.
[1950-55]

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also known as regular polyhedron

Geometric solid all of whose faces are identical regular polygons and all of whose angles are equal.

There are only five such polyhedrons. The cube is constructed from the square, the dodecahedron from the regular pentagon, and the tetrahedron, octahedron, and icosahedron (with 20 faces) from the equilateral triangle. They are known as the Platonic solids because of Plato's attempt to relate each to one of the five elements that he believed formed the world.

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any of the five geometric solids whose faces are all identical, regular polygons meeting at the same three-dimensional angles. Also known as the five regular polyhedra, they consist of the tetrahedron (or pyramid), cube, octahedron, dodecahedron, and icosahedron. Pythagoras (c. 580–c. 500 BC) probably knew the tetrahedron, cube, and dodecahedron. According to Euclid (fl. c. 300 BC), the octahedron and icosahedron were first discussed by the Athenian mathematician Theaetetus (c. 417–369 BC). However, the entire group of regular polyhedra owes its popular name to the great Athenian philosopher Plato (428/427–348/347 BC), who in his dialogue Timaeus associated them with the four basic elements—fire, air, water, and earth—that he supposed to form all matter through their combinations. Plato assigned the tetrahedron, with its sharp points and edges, to the element fire; the cube, with its four-square regularity, to earth; and the other solids concocted from triangles (the octahedron and the icosahedron) to air and water, respectively. The one remaining regular polyhedra, the dodecahedron, with 12 pentagonal faces, Plato assigned to the heavens with its 12 constellations. Because of Plato's systematic development of a theory of the universe based on the five regular polyhedra, they became known as the Platonic solids.

Euclid devoted the last book of the Elements to the regular polyhedra, which thus serve as so many capstones to his geometry. In particular, his is the first known proof that exactly five regular polyhedra exist. Almost 2,000 years later the astronomer Johannes Kepler (Kepler, Johannes) (1571–1630) resuscitated the idea of using the Platonic solids to explain the geometry of the universe in his first model of the cosmos. The symmetry, structural integrity, and beauty of these solids have inspired architects, artists, and artisans from ancient Egypt to the present.

J.L. Heilbron

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Universalium. 2010.

### См. также в других словарях:

• Platonic solid — In geometry, a Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex; thus, all… …   Wikipedia

• Platonic solid — noun any one of five solids whose faces are congruent regular polygons and whose polyhedral angles are all congruent • Syn: ↑regular polyhedron, ↑regular convex solid, ↑regular convex polyhedron, ↑Platonic body, ↑ideal solid • Hypernyms:… …   Useful english dictionary

• Platonic solid — noun Any one of the following five polyhedra: the regular tetrahedron, the cube, the regular octahedron, the regular dodecahedron and the regular icosahedro …   Wiktionary

• Platonic solid — (also Platonic body) noun one of five regular solids (a tetrahedron, cube, octahedron, dodecahedron, or icosahedron) …   English new terms dictionary

• platonic solid — /plətɒnɪk ˈsɒləd/ (say pluhtonik soluhd) noun any one of the five regular polyhedrons (tetrahedron, hexahedron, octahedron, dodecahedron, icosahedron) …   Australian-English dictionary

• Platonic hydrocarbon — Platonic hydrocarbons are the molecular representation of platonic solid geometries with vertices replaced by carbon atoms and with edges replaced by chemical bonds. Not all platonic solids have a molecular counterpart:* Tetravalent carbon… …   Wikipedia

• Platonic body — noun any one of five solids whose faces are congruent regular polygons and whose polyhedral angles are all congruent • Syn: ↑regular polyhedron, ↑regular convex solid, ↑regular convex polyhedron, ↑Platonic solid, ↑ideal solid • Hypernyms:… …   Useful english dictionary

• Platonic — Plato s influence on Western culture was so profound that several different concepts are linked by being called platonic or Platonist, for accepting some assumptions of Platonism, but which do not imply acceptance of that philosophy as a whole.… …   Wikipedia

• solid — solidly, adv. solidness, n. /sol id/, adj. 1. having three dimensions (length, breadth, and thickness), as a geometrical body or figure. 2. of or pertaining to bodies or figures of three dimensions. 3. having the interior completely filled up,… …   Universalium

• Platonic — adjective Of or relating to the ancient Greek philosopher Plato or his philosophies. See Also: Plato, Platonically, Platonism, Platonist, Platonistic, Platonic body, Platonic hydrocarbon, Platonic solid …   Wiktionary

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