# Definitions for polytopepo·ly·tope

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1. polytopenoun

A finite region of n-dimensional space bounded by hyperplanes; the geometrical entity represented by the general term of the infinite sequence "point, line, polygon, polyhedron, ...".

2. Etymology: From poly- + -tope

### WikipediaRate this definition:0.0 / 0 votes

1. Polytope

In elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in any general number of dimensions n as an n-dimensional polytope or n-polytope. For example, a two-dimensional polygon is a 2-polytope and a three-dimensional polyhedron is a 3-polytope. In this context, "flat sides" means that the sides of a (k + 1)-polytope consist of k-polytopes that may have (k – 1)-polytopes in common. Some theories further generalize the idea to include such objects as unbounded apeirotopes and tessellations, decompositions or tilings of curved manifolds including spherical polyhedra, and set-theoretic abstract polytopes. Polytopes of more than three dimensions were first discovered by Ludwig Schläfli before 1853, who called such a figure a polyschem. The German term polytop was coined by the mathematician Reinhold Hoppe, and was introduced to English mathematicians as polytope by Alicia Boole Stott.

### WikidataRate this definition:0.0 / 0 votes

1. Polytope

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. Some theories further generalize the idea to include such things as unbounded polytopes, and abstract polytopes. When referring to an n-dimensional generalization, the term n-polytope is used. For example, a polygon is a 2-polytope, a polyhedron is a 3-polytope, and a polychoron is a 4-polytope. The term was coined by the mathematician Hoppe, writing in German, and was later introduced to the English Mathematicians by Alicia Boole Stott, the daughter of logician George Boole.

### Numerology

1. Chaldean Numerology

The numerical value of polytope in Chaldean Numerology is: 7

2. Pythagorean Numerology

The numerical value of polytope in Pythagorean Numerology is: 7

### Popularity rank by frequency of use

polytope#10000#83617#100000

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"polytope." Definitions.net. STANDS4 LLC, 2024. Web. 9 Aug. 2024. <https://www.definitions.net/definition/polytope>.

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