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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.



Polyhedra can be convex or concave.

Number of sides

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:


Prisms and pyramids can be polyhedra.

Surface area

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


The volume of a certain polyhedron is defined as $(B)h$, where B is the area of the base of the polyhedron and h is the height to this base.


Related figures

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

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