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A polyhedra, in three dimensions, refers to a solid in three-dimensional space with flat polygonal faces, straight edges, and sharp corners or vertices. These geometric shapes are the three-dimensional counterparts to polygons in two dimensions. The simplest polyhedra are the Platonic solids, which are convex, regular polyhedra where all faces are congruent regular polygons and the same number of faces meet at each vertex. There are exactly five Platonic solids: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.

Beyond the Platonic solids, there are many other types of polyhedra. Convex polyhedra are those where the line segment connecting any two points within the polyhedron lies entirely within the polyhedron. Non-convex or concave polyhedra have at least one indentation. Archimedean solids are semi-regular polyhedra, featuring regular polygons of two or more types as faces, with the same arrangement of polygons around each vertex. Johnson solids are convex polyhedra with regular polygonal faces but without the symmetry constraints of Platonic or Archimedean solids.

The study of polyhedra is a fundamental part of geometry and has applications in various fields, including crystallography, architecture, computer graphics, and the design of molecules. Understanding the properties of polyhedra involves concepts like Euler's formula, which relates the number of vertices, edges, and faces of a convex polyhedron (V - E + F = 2).