This is one of the Platonic solids, and is treated in the article Polyhedron, as is also the derived **Archimedean** solid named the "truncated tetrahedron"; in addition, the regular tetrahedron has important crystallographic relations, being the hemihedral form of the regular octahedron and consequently a form of the cubic system.

He was the author of numerous inventions, including the cagniardelle, a blowing machine, which consists essentially of an **Archimedean** screw set obliquely in a tank of water in such a way that its lower end is completely and its upper end partially immersed, and operated by being rotated in the opposite direction to that required for raising water.

(2) A right cylinder having for its base an **Archimedean** spiral is intersected by a right circular cone which has the generating line of the cylinder passing through the initial point of the spiral for its axis.

The "regular icosahedron" is one of the Platonic solids; the "great icosahedron" is a Kepler-Poinsot solid; and the "truncated icosahedron" is an **Archimedean** solid (see Polyhedron).

The blanks are charged into a hopper at one end of the furnace and conveyed towards the other end by a revolving **Archimedean** screw.

The mensuration of the cube, and its relations to other geometrical solids are treated in the article Polyhedron; in the same article are treated the **Archimedean** solids, the truncated and snubcube; reference should be made to the article Crystallography for its significance as a crystal form.

The "small stellated dodecahedron," the "great dodecahedron" and the "great stellated dodecahedron" are Kepler-Poinsot solids; and the "truncated" and "snub dodecahedra" are **Archimedean** solids (see Polyhedron).