If you are being introduced to this topic for the first time, your first question might well be ‘What is a polyhedron?’ You may recall that geometry itself is sometimes (not too exactly) defined as the study of space or of figures in space—two dimensional for plane geometry and three for solid geometry. The idea of sets is perhaps familiar also. If you use the language of sets, a plane figure may be defined as a set of line segments enclosing a portion of two-dimensional space. Such a plane figure is called a polygon. A polyhedron is then defined as a set of plane figures enclosing a portion of three-dimensional space.

All the terms used in this subject are derived from classical Greek. Plato, the famous Greek philosopher, left the imprint of this thought deeply fixed in Euclid's Elements. This ancient book, for centuries the only textbook of geometry, was concerned with ‘ideal’ lines and ‘ideal’ figures. The ideal lines are straight and the ideal polygons are regular, that is, they have all sides and all angles equal. The simplest regular polygon is the equilateral triangle. It is the simplest because it has the least number of line segments possible to enclose a portion of two-dimensional space. It is an interesting fact that Euclid's Elements begins with a proposition describing how to construct an equilateral triangle and ends with a study of the five regular solids. Each of these has regular polygons of the same kind for all its faces. They are known today as the five Platonic solids. The tetrahedron, which has four equilateral triangles for its faces, is the three-dimensional analogue of the two-dimensional equilateral triangle. It is the simplest polyhedron, since it has the least number of faces possible to enclose a portion of three-dimensional space.

With the equilateral triangle the following polygons enter the picture: the square (four sides), the pentagon (five sides), the hexagon (six sides), the octagon (eight sides) and the decagon (ten sides), all of course only as regular polygons.