Difference between revisions of "Polyhedron"
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| − | A polyhedron is a three-dimensional surface composed of at least four flat [[face]]s which encloses a region of [[space]]. These faces intersect in [[edge]]s and [[vertex|vertices]]. Polyhedra are 3-D analogues of [[polygon]]s. They can be thought of as sets of ordered triples. | + | A polyhedron is a three-dimensional surface composed of at least four flat [[face]]s which encloses a region of [[space]]. These faces intersect in [[edge]]s and [[vertex|vertices]]. Polyhedra are 3-D analogues of [[polygon]]s. They can be thought of as sets of [[ordered]] triples. |
== Classification == | == Classification == | ||
Revision as of 19:56, 27 September 2007
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.
Contents
Classification
Concavity
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:
- 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.
Volume
Angles
Related figures
- Polyhedral solids are the union of a polyhedron and the space that it encloses.
- Polygons
- Polytopes
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