Regular Polyhedrons

Excerpts

• Regular Polyhedrons

  A polyhedron is *convex* if every section of it made by a plane is a convex polygon.

• Regular Polyhedrons

  These names are all derived from the Greek and refer to the number of faces.

• Regular Polyhedrons

  The faces, edges, and vertices taken together form the surface of the polyhedron.

• Regular Polyhedrons

  From these propositions it follows that each of the polyhedral angles of a regular polyhedron may be formed by three, four, or five (but not six) equilateral triangles; by three (but not four) squares; or by three (but not four) regular pentagons.

• Regular Polyhedrons

  *The sum of the face angles of a polyhedral angle is less than $360$°*.

• Regular Polyhedrons

  At the center $E$ of an equilateral triangle $ABC$ erect a perpendicular to the plane of the triangle.

Equations

• Regular Polyhedrons

  AD = AC

  In the construction of the regular tetrahedron, the fourth vertex D is placed on the perpendicular at E so that its distance from A equals the side AC.

• Regular Polyhedrons

  AF = AE = AB

  In the construction of the regular octahedron, the two apex points E and F are placed on the perpendicular through the center O so that each is at distance AB, the side of the square, from A.

Problems

No exercises in this chapter.