HEXAEDRON

, or Hexahedron, one of the five regular or Platonic bodies; being indeed the same as the cube; and is so called from its having 6 faces.— The square of the side or edge of a Hexahedron, is onethird of the square of the diameter of the circumscribing sphere: and hence the diameter of a sphere is to the side of its inscribed Hexahedron, as √3 to 1.

In general, if A, B, and C be put to denote respectively the linear side, the surface, and the solidity of a Hexahedron or cube, also r the radius of the inscribed sphere, and R the radius of the circumscribed one; then we have these general equations or relations: 1. . 2. . 3. . 4. . 5. .