# 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. .