Editing Regular polyhedron (section)

=== Greeks ===

The earliest known ''written'' records of the regular convex solids originated from Classical Greece. When these solids were all discovered and by whom is not known, but [[Theaetetus (mathematician)|Theaetetus]] (an [[Athens|Athenian]]) was the first to give a mathematical description of all five (Van der Waerden, 1954), (Euclid, book XIII). [[H.S.M. Coxeter]] (Coxeter, 1948, Section 1.9) credits [[Plato]] (400 BC) with having made models of them, and mentions that one of the earlier [[Pythagoreans]], [[Timaeus of Locri]], used all five in a correspondence between the polyhedra and the nature of the universe as it was then perceived – this correspondence is recorded in Plato's dialogue [[Timaeus (dialogue)|''Timaeus'']]. Euclid's reference to Plato led to their common description as the ''Platonic solids''.

One might characterise the Greek definition as follows:
*A regular polygon is a ([[Convex polygon|convex]]) planar figure with all edges equal and all corners equal.
*A regular polyhedron is a solid (convex) figure with all faces being congruent regular polygons, the same number arranged all alike around each vertex.

This definition rules out, for example, the [[square pyramid]] (since although all the faces are regular, the square base is not congruent to the triangular sides), or the shape formed by joining two tetrahedra together (since although all faces of that [[triangular bipyramid]] would be equilateral triangles, that is, congruent and regular, some vertices have 3 triangles and others have 4).

This concept of a regular polyhedron would remain unchallenged for almost 2000 years.