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In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex. There are only five such polyhedra:
العربية; Asturianu; Azərbaycanca; 閩南語 / Bân-lâm-gú; Беларуская; Беларуская (тарашкевіца) Català; Чӑвашла
Platonic love, a relationship that is not sexual in nature; Platonic forms, or the theory of forms, Plato's model of existence; Platonic idealism; Platonic solid, any of the five convex regular polyhedra; Platonic crystal, a periodic structure designed to guide wave energy through thin plates; Platonism, the philosophy of Plato (Classical period)
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 ...
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 ...
There are five convex regular polyhedra, known as the Platonic solids. All Platonic solids have circumscribed spheres. All Platonic solids have circumscribed spheres. For an arbitrary point M {\displaystyle M} on the circumscribed sphere of each Platonic solid with number of the vertices n {\displaystyle n} , if M A i {\displaystyle MA_{i}} are ...
Name picture Faces Edges Vertices Vertex configuration icosidodecahedron (quasi-regular: vertex- and edge-uniform) (32: 20 triangles 12 pentagons: 60: 30 3,5,3,5
[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]