# polytope

## EnglishEdit

### EtymologyEdit

From German *Polytop*, equivalent to *poly-* (“many”) + *-tope* (“surface”). Coined by Hoppe in 1882 and introduced to English by Alicia Boole Stott.^{[1]}

### NounEdit

**polytope** (*plural* **polytopes**)

- (geometry) A finite region of
*n*-dimensional space bounded by hyperplanes (a geometric shape with flat sides, existing in any number of dimensions); the geometrical entity represented by the general term of the infinite sequence "point, line, polygon, polyhedron, ...".**1964**, Victor Klee,*On the Number of Vertices of a Convex Polytope*,*Canadian Journal of Mathematics*, Volume XVI, Number 4, page 701,- As is well known, the theory of linear inequalities is closely related to the study of convex
**polytopes**.

- As is well known, the theory of linear inequalities is closely related to the study of convex
**1998**, F. Pierrot, M. Benoit, P. Dauchez,*SamoS: A Pythagorean Solution for Omnidirectional Underwater Vehicles*, Jadran Lenar I, Manfred L. Husty (editors),*Advances in Robot Kinematics: Analysis and Control*, page 220,- This
**polytope**is mapped into a Cartesian force**polytope**(*resp.*torque**polytope**) in the Cartesian space. Such a**polytope**represents the exact force (*resp.*torque) that can be produced on the vehicle main body.

- This
**2006**, Rekha R. Thomas,*Lectures in Geometric Combinatorics*, page 27,- Verify the Hirsch conjecture for the 3-cube, 4-cube and any other
**polytope**that takes your fancy. - The Steinitz theorem is a very satisfactory understanding of the graphs of three-dimensional
**polytopes**.

- Verify the Hirsch conjecture for the 3-cube, 4-cube and any other

#### HyponymsEdit

- (geometrical figure): polygon (2d figure), polyhedron (3d figure), hypercube (generalised cube), simplex (generalised tetrahedron), tesseract (4d cube)

#### TranslationsEdit

geometric shape

### ReferencesEdit

- ^
**1910**, A. Boole Stott,*Geometrical deduction of semiregular from regular polytopes and space fillings*, Verhandelingen of the Koninklijke academy van Wetenschappen width unit Amsterdam, Eerste Sectie 11,1, Amsterdam.