Polyhedron

A polyhedron is a three-dimensional surface composed of at least four flat faces which encloses a region of space. These faces intersect in edges and vertices. Polyhedra are 3-D analogues of polygons. They can be thought of as sets of ordered triples.

Classification

Concavity

Polyhedra can be convex or concave]].

Regular polyhedra

They have congruent faces, angles, and edges. Only regular tetrahedra, hexahedra (cubes), octahedra, dodecahedra, and icosahedra exist. (In addition, a sphere could be thought of a polyhedron with an infinite number of faces.)

Common polyhedra

The polyhedra most commonly encountered include:

• tetrahedron - 4 faces
• hexahedron - 6 faces

etc.

Prisms and pyramids can be polyhedra.

Surface area

The surface area of a polyhedron is the sum of its sides.

Related figures

• Polyhedral solids are the union of a polyhedron and the space that it encloses.
• Polygons
• Polytopes

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