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.
Related terms Translations
  • French: polytope
  • German: Polytop
  • Italian: politopo
  • Portuguese: politopo
  • Russian: полиэ́др
  • Spanish: politopo

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