solidi

Solidi is the plural form of solid in several Romance languages, notably Italian, and in mathematics the term refers to three-dimensional objects with volume. A solid is bounded in three dimensions by surfaces and has length, width, and height. In geometry, solids are studied for properties such as volume, surface area, and cross sections, and they contrast with two-dimensional shapes and with curves.

Solidi are commonly classified as convex or non-convex. Simple convex solids include common shapes such as prisms, pyramids, cylinders, cones, and spheres. The regular, or Platonic, solids are the five convex polyhedra with congruent faces: tetrahedron, cube (hexahedron), octahedron, dodecahedron, and icosahedron. More generally, polyhedra are bounded by polygonal faces; curved solids such as spheres and cylinders are also treated as solids.

Key measurements include volume and surface area. Formulas recur: prism volume base area times height; pyramid and cone volumes are one third of base area times height; cylinder volume is base area times height; sphere volume is 4/3 pi r^3, surface area 4 pi r^2.

In physics, solids are one of the states of matter characterized by structural rigidity and defined mechanical properties; crystalline solids have long-range order, while amorphous solids lack it. Solidi have wide applications in geometry, architecture, computer graphics, and engineering, where three-dimensional modeling and analysis are essential.