The octahedron, one of the classic polyhedrons, is enclosed by eight equilateral triangles. If you put a tripartite pyramid on each triangle you get a diversity of complex polyhedral forms. And if you do this a second time, you will see polyhedral forms of stars.
Because of their manifold symmetry, the regular polyhedrons have been well known since ancient times as the geometric objects of the highest degree of simplicity and beauty. They are the basis of countless complex polyhedra, with computer graphics methods that are easy to create.
Wolfram Demonstrations Project
Published: March 7 2011