A regular tetrahedron is one in which all four faces are equilateral triangles. It has been known since antiquity and is one of the five regular Platonic solids. In a regular tetrahedron, not only are all its faces the same size and shape (congruent) but so are all its vertices and edges. Together with the regular octahedron, these two solids can be packed alternately to fill space, however regular tetrahedra alone cannot fill space. Five tetrahedra are laid flat on a plane, with the highest 3-dimensional points marked as 1, 2, 3, 4, and 5. These points are then attached to each other and a thin volume of empty space is left, where the five edge angles do not quite meet. The regular tetrahedron is self-dual, which means that its dual is another regular tetrahedron. The compound figure comprising two such dual tetrahedra form a stellated octahedron or stella octangula. [Tetrahedron. Wikipedia]