polytope

Etymology

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

noun

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, ...".
   As is well known, the theory of linear inequalities is closely related to the study of convex polytopes. 1964, Victor Klee, On the Number of Vertices of a Convex Polytope: Canadian Journal of Mathematics, volume XVI, number 4, page 701
   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. 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
   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. 2006, Rekha R. Thomas, Lectures in Geometric Combinatorics, page 27