polytopeとは 意味・読み方・使い方

語源

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

発音

• (英国発音) IPA: /ˈpɒlɪtəʊp/, /ˈpɒliːˌtəʊp/
• (米国発音) IPA: /ˈpɑliˌtoʊp/
• ハイフネーション: pol‧y‧tope
• 韻: -ɒlɪtəʊp, -ɒliːtəʊp

名詞

polytope (plural polytopes)

1. (geometry) A geometric shape (of any number of dimensions) which is fully enclosed and has flat sides, making it a member of the generalized class of shapes which includes the two-dimensional polygon and three-dimensional polyhedron; (formally) a finite region of n-dimensional space bounded by hyperplanes.
   • 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.

下位語

派生語

関連する語

• polytopic

参照