The Compendium Geometry is an eBook providing facts, formulas and explanations about geometry.


A (regular) tetrahedron is a polyhedron composed of four equilateral triangular faces, three of which meet at each vertex. It is one of the Platonic solids.

The tetrahedron has 7 axes of symmetry: 4 C3 (axes connecting vertices with the centers of the opposite faces) and 3 C2 (the axes connecting the midpoints of opposite sides).

The height h of the tetrahedron is defined by

h = a/

The volume V of the tetrahedron is given by

V = Abh/3 = a3/12

with Ab being the area of the base triangle. The surface area S of the tetrahedron is

S = a2

The radii of the circumscribed (rc) and inscribed (ri) spheres are

rc = a/4 and ri = a/12, respectively.

Last Update: 2010-12-06