polytope

English

A 3-dimensional Stasheff polytope

Etymology

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

Pronunciation

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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”, in 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.

Hyponyms

• (geometrical figure): polygon (2D figure), polyhedron (3D figure), polychoron (4D figure), hypercube (generalised cube), simplex (generalised tetrahedron), tesseract (4D cube)

Derived terms

• 4-polytope
• cross-polytope

Related terms

• polytopic

Translations

geometric shape

• Catalan: polítop m
• Chinese:

  Mandarin: 多胞形 (zh) (duōbāoxíng)

• Esperanto: hiperpluredro
• French: polytope (fr) m
• German: Polytop m
• Hungarian: politóp (hu)
• Italian: politopo (it) m
• Japanese: ポリトープ (poritōpu), 超多面体 (ちょうためんたい, chōtamentai)
• Korean: 다포체(多胞體) (dapoche)
• Persian: چندبر (fa)
• Polish: wielotop m, wielokomórka f
• Portuguese: politopo m
• Russian: полиэ́др (ru) m (poliédr), полито́п (ru) m (politóp)
• Spanish: politopo m
• Swedish: polytop (sv) c

French

Pronunciation

• Audio:

  (file)

Noun

polytope m (plural polytopes)

1. polytope