# polytope

## English

A 3-dimensional Stasheff polytope

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### Etymology

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

### Noun

polytope (plural polytopes)

1. (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.
• 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.
• 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.

### References

1. ^ 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.

## French

### Noun

polytope m (plural polytopes)

1. polytope