OCTAEDRON

, or Octahedron, one of the five regular bodies; contained under 8 equal and equilateral triangles.—It may be conceived as consisting of two quadrilateral pyramids joined together at their bases.

To form an Octaedron. Join together 8 equal and equilateral triangles, as in fig. 1; then cut the lines half through, and fold the figure up by these cut lines, till the extreme edges meet, and form the Octaedron, as in figure 2.

In an Octaedron, if A be the linear edge or side, B its whole surface, C its solidity, or solid content, R the radius of the circumscribed sphere, and r the radius of the inscribed sphere: Then .

See my Mensuration, pa. 251 &c, 2d edition.