The regular and symmetrical nature of a platonic solid also means that it is relatively straightforward to find its surface area or volume. The radii of the spheres are called the circumradius, the midradius, and the inradius respectively. For each of the platonic solids, these three spheres are concentric (i.e. a sphere that is completely enclosed by the platonic solid, and that is tangent to each of its faces). a sphere that is tangent to each of the edges of the platonic solid), and an inscribed sphere or insphere (i.e. a sphere that completely encloses the platonic solid, and for which all of the vertices of the platonic solid lie on the surface of the sphere), a midsphere (i.e. For each platonic solid, it is possible to construct a circumscribed sphere or circumsphere (i.e. Note that, since the names used for the platonic solids are based on the number of faces each one has, these same names may be used to describe other three-dimensional solids that have the same number of faces.Ĭharacteristics of the Platonic Solids NameĪs well as the features described above, the regularity of the platonic solids means that they are all highly symmetrical. The main characteristics of the platonic solids are summarised in the table below. Greek mathematician Euclid is believed to have drawn on the work of Theaetetus when writing the complete mathematical description of the platonic solids which appears in his later work, the Elements. One of Plato's contemporaries, the classical Greek mathematician Theaetetus, is credited with having formulated a mathematical description of all five platonic solids. In Plato's writings, the dodecahedron appears to be related to the arrangement of the constellations - perhaps a reference to the signs of the zodiac, although his exact meaning is not completely understood. He is believed to have associated four of them (the tetrahedron, cube, octahedron and icosahedron) with the four classical elements ( fire, earth, air, and water). Plato is known to have written about the shapes we know today as the platonic solids, although not in a particularly mathematical context. The term platonic is derived from the name of the Greek philosopher Plato, who is believed to have lived from around 423 to 347 BCE. The names of the platonic solids reflect the number of faces that each one possesses.
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