On Platonic solids: regular three-dimensional geometric objects with flat faces and straight edges
Platonic solids have been known since ancient Greece. Plato described them in detail in one of his works. There are exactly five Platonic solids, a fact proven by Plato's contemporary, Theaetetus.
Platonic solids are defined as polyhedra bounded exclusively by identical regular polygons. A polyhedron is a solid with flat faces. A polygon is a plane figure with straight edges. In a Platonic solid, every vertex, every edge and every face is identical. Although the definition allows for any type of polygon, only three distinct types appear in Platonic solids. The equilateral triangle is found in three of them, the square is found in one and the regular pentagon also in one. There are no perfectly regular three-dimensional solids with other types of polygons as faces.
The names of the Platonic solids are derived from the Greek words for the number of their faces, such as tetra for four. However, the hexahedron (six-faced solid) is usually referred to as a cube. Strictly speaking, a term like tetrahedron should be preceded by the adjective regular when referring to a Platonic solid, as there are also tetrahedra with non-identical faces, edges, and vertices. In practice, however, this qualifier is usually omitted, and the shape is simply referred to as a general tetrahedron.
The Platonic solids are typically ordered according to the number of their faces. The tetrahedron has the fewest vertices, while the icosahedron has the most, with twenty. The dodecahedron, which has twelve faces, features the highest number of vertices per face, with five. Platonic solids occur in nature, for example, approximately in the form of crystals. The dodecahedron appears rather rarely, whereas the others are quite common there.