Dodecahedron

is one of the platonic bodies, or five regular solids, and is contained under 12 equal and regular pentagons. The solidity of a dodecahedron , is found by multiplying the area of one of the pentagonal faces of it by 12; and this latter product by ¹⁄₃d of the distance of the face from the centre of the dodecahedron , which is the same as the centre of the circumscribing sphere. The side of a dodecahedron inscribed in a sphere, is the greater part of the side of a cube inscribed in that sphere, cut into extreme and mean proportion. If the diameter of the sphere be 1,0000, the side of a dodecahedron inscribed in it will be.35682 nearly. All dodecahedrons are similar, and are to one another as the cubes of the sides; and their surfaces are also similar, and therefore they are as the squares of their sides; whence as.509282 is to 10.51462, so is the square of the side of any dodecahedron to the superficies thereof; and as .3637 is to 2.78516, so is the cube of the side of any dodecahedron to the solidity of it.