Concept
Platonic solid
Overview
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: a regular tetrahedron (four triangular faces), a cube (six square faces), a regular octahedron (eight triangular faces), a regular dodecahedron (twelve pentagonal faces), and a regular icosahedron (twenty triangular faces).
Geometers have studied the Platonic solids for thousands of years. They are named for the ancient Greek philosopher Plato, who hypothesized in one of his dialogues, the Timaeus, that the classical elements were made of these regular solids.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
Those bodies which are called SOLIDS, receive into their composition a great number of homogeneous, similar, and analogous particles, disposed to unite themselves with energies conspiring or tending to the same point. The primitive beings, or elements of bodies, have need of supports, of props; that is to say, of the presence of each other, for the purpose of preserving themselves; of acquiring consistence or…
Paul Henri Thiry Holbach, The System of Nature, or, the Laws of the Moral and Physical World. Volume 1
States what Platonic solid is.
The former we call soft, the latter hard, bodies. In some bodies the parts are so very easily separable, that they not only yield to a very moderate pressure, but easily receive the pressing body within them, and without much resistance allow it to traverse their extent in every possible direction. These are called Fluid, in contradistinction to those of which the parts not being so easily separable, are upon that…
Adam Smith, The Essays of Adam Smith
States what Platonic solid is.
Now geometrically regular figures, such as a circle, a square, a cube, etc., are commonly adduced by critics of taste as the simplest and most indisputable examples of beauty; and yet they are called regular, because we can only represent them by regarding them as mere presentations of a definite concept which prescribes the rule for the figure (according to which alone it is possible). One of these two must be…
Immanuel Kant, Kant's Critique of Judgement
States what Platonic solid is.
Philosophers who discussed Platonic solid
Related ideas
- Manchester University Press
- Golden ratio
- Harmonice Mundi
- Johannes Kepler
- Kepler's laws of planetary motion
- Neoclassicism
- Geometry
- Virus
- Group (mathematics)
- Aether (classical element)
- Mercury (planet)
- Meteorology
- Martin Gardner
- Planet
- Plato
- Pythagoras
- Euclid's Elements
- Proclus
- Solar System
- Scotland
- Topology
- Tetrahedron
- Aristotle
- Baruch Spinoza
Place in the tradition
Part of Pythagoreanism.