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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 ...
العربية; Asturianu; Azərbaycanca; 閩南語 / Bân-lâm-gú; Беларуская; Беларуская (тарашкевіца) Català; Чӑвашла
Truncated icosahedron, one of the Archimedean solids illustrated in De quinque corporibus regularibus. The five Platonic solids (the regular tetrahedron, cube, octahedron, dodecahedron, and icosahedron) were known to della Francesca through two classical sources: Timaeus, in which Plato theorizes that four of them correspond to the classical elements making up the world (with the fifth, the ...
Simple English; Slovenčina ... The best known is the (convex, non-stellated) regular icosahedron—one of the Platonic solids—whose faces are 20 equilateral triangles.
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.
Each convex regular 4-polytope is bounded by a set of 3-dimensional cells which are all Platonic solids of the same type and size. These are fitted together along their respective faces (face-to-face) in a regular fashion, forming the surface of the 4-polytope which is a closed, curved 3-dimensional space (analogous to the way the surface of ...
The carved stone balls have been taken as evidence of knowledge of the five Platonic solids a millennium before Plato described them. Indeed, some of them exhibit the symmetries of Platonic solids, but the extent of this and how much it depends on mathematical understanding is disputed, as configurations resembling the solids can naturally ...
[3] Aristotle also postulated that the heavens were made of a fifth element, which he called aithêr (aether in Latin, ether in American English). [4] Following its attribution with nature by Plato, Johannes Kepler in his Harmonices Mundi sketched each of the Platonic solids, one of them is a regular dodecahedron. [5]