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Polyhedra are three-dimensional shapes with flat polygonal faces, straight edges, and vertices where edges meet. The study of polyhedra is a branch of mathematics known as polyhedral geometry. Polyhedra are classified based on their faces, edges, and vertices. The simplest polyhedron is the tetrahedron, which has four triangular faces. More complex polyhedra include the cube (six square faces), the octahedron (eight triangular faces), the dodecahedron (twelve pentagonal faces), and the icosahedron (twenty triangular faces). These are known as the Platonic solids, named after the ancient Greek philosopher Plato who studied them.

Polyhedra can also be classified based on their symmetry. Regular polyhedra have congruent faces and identical vertices, while semi-regular polyhedra have two or more types of faces. Archimedean solids are a type of semi-regular polyhedron, named after the ancient Greek mathematician Archimedes. These solids have congruent vertices but may have more than one type of face.

Polyhedra have applications in various fields, including architecture, engineering, and computer graphics. They are used to model complex shapes and structures, and their properties are studied in mathematics and physics. The study of polyhedra continues to be an active area of research, with new discoveries and applications being made regularly.