poliédricas

Poliédricas (polyhedral) refers to polyhedra, three-dimensional solids bounded by flat polygonal faces, joined by straight edges and meeting at vertices. A polyhedron is defined by a finite set of polygons arranged so they enclose a closed surface. The study of poliédrica encompasses a wide range of forms, from highly regular to irregular, and its concepts appear in geometry, crystallography, and chemistry.

Polyhedra are commonly classified by shape, symmetry, and topology. They can be convex, having every line segment between two points inside the solid lie inside as well, or non-convex (including star-like forms). Regular polyhedra have identical faces and identical vertices; the five Platonic solids—tetrahedron, cube, octahedron, dodecahedron, and icosahedron—are the classic examples, each with a Schläfli symbol {p,q} describing the face type and vertex arrangement. More general families include semi-regular (Archimedean) solids with uniform vertex figures and 13 distinct shapes, and their duals, the Catalan solids. Regular non-convex polyhedra, the Kepler-Poinsot solids, extend the concept to star forms.

Key properties include Euler’s formula, V − E + F = 2 for convex polyhedra and other simple topologies; this relation generalizes to any polyhedron homeomorphic to a sphere. Polyhedra are connected to graph theory through polyhedral graphs, which are planar and three-connected in many cases. Duality links polyhedra to their duals, exchanging faces and vertices while preserving edge structure.

Applications and appearances span architecture, crystallography, and chemistry (for example, fullerenes like C60), as well as traditional objects such as dice and geodesic domes.