IV.3.1 The Tetrahedron
A regular Tetrahedron is one in which all four faces are equilateral triangles. It is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces. It has four vertices, six edges and four triangular faces, and that s why it is also known as a triangular pyramid. For any Tetrahedron there exists a sphere, called the circumsphere, on which all four vertices lie, and another sphere, called the insphere, tangent to its faces. Like all convex polyhedra, a Tetrahedron can be folded from a single sheet of paper.
The regular Tetrahedron is self-dual, which means that its dual is itself, and the compound figure comprising two such dual tetrahedra form a stellated Octahedron or stella octangula, which means eight-pointed star . Unlike to what Plato suggested, this distinctive property of Tetrahedron makes it correspond to Quintessence, in addition to its being the simplest of them all. Just like the four elements, two of the other four solid are the duals of the other two, as we shall see further below.
Figure IV.4: The Tetrahedron has four faces, which are equilateral triangles, and four vertices, and six edges. It is the dual of itself, and it is also called a triangular pyramid.