In elementary geometry, a polytope is a geometric object with flat sides, which exists in any general number of dimensions. A polygon is a polytope in two dimensions, a polyhedron in three dimensions, and so on in higher dimensions (such as a polychoron in four dimensions). Some theories further generalize the idea to include such objects as unbou...
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http://en.wikipedia.org/wiki/Polytope
A bounded polyhedron.
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http://glossary.computing.society.informs.org/index.php?page=P.html
(from the article `combinatorics`) A (convex) polytope is the convex hull of some finite set of points. Each polytope of dimensions has as faces finitely many polytopes of dimensions ... In four-dimensional space there exist exactly six regular polytopes, five of them generalizations from three-dimensional space. In any space of more ....
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http://www.britannica.com/eb/a-z/p/91
A higher-dimensional analogue of a polygon or polyhedron. The number of possible regular polytopes depends on the number of dimensions. In two dimensions there are infinitely many possible regular polygons; in three dimensions there are five possible regular polyhedra; in four dimensions there are s...
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http://www.daviddarling.info/encyclopedia/P/polytope.html
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