Tetrahedron

A tetrahedron is a pyramidal polyhedral structure in which a triangular base is surmounted by three triangular sides which meet at a common apex. In a regular tetrahedron, all 4 of the triangular faces are equilateral. A regular tetrahedron is one of the five Platonic Solids, and the one with the smallest number of faces and smallest number of vertices.

Geometry

The volume of a triangular-based pyramid:

<math>V= \frac{1}{3}Bh</math>

V is the overall volume of a pyramid. B equals the area of the base, and h is the perpendicular height.

Religious connection

Some people ascribe religious or mystical properties to the tetrahedron. An excellent mathematical illustration of the unity of the Trinity is the geometrical form of the triangular three-sided regular tetrahedron, an undivided pyramidal construct of a single, indivisible point extending into three joint equilateral triangular faces simultaneously united to a single triangular base. This is especially evident when an equilateral tetrahedron is made of flawless transparent crystal. Through any one face of the crystal form each of the other sides is clearly visible. Each of the faces is a distinctly different face (they cannot be the same face) but all of them have exactly the same shape, the same size, and the same substance. What is predicated of any one of them is predicated of each of them. A tetrahedral crystal displayed standing on the flat surface of the jeweler's counter or the shelf of a display case cannot exist without three faces inseparably existing as extending from the single, undivided point of one apex to the same undivided triangular base situated on the surface or foundation on which it stands: a single crystal, not three, with three faces, not one. No matter how it is turned or rotated, it always looks the same and remains the same.