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A 3-dimensional Stasheff polytope
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From German Polytop, equivalent to poly- (many) + -tope (surface). Coined by Hoppe in 1882 and introduced to English by Alicia Boole Stott.[1]


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.


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  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.



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polytope m (plural polytopes)

  1. polytope