polytope

Definition

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.

Etymology

Learned borrowing from German Polytop, originally coined by German mathematician Reinhold Hoppe in 1882, and first used in English by British mathematician Alicia Boole Stott in her 1910 paper Geometrical deduction of semiregular from regular polytopes and space fillings. By surface analysis, poly- (“many”) + -tope (“surface”), from Ancient Greek τόπος (tópos, “region; area”).

Example Sentences

• "As is well known, the theory of linear inequalities is closely related to the study of convex polytopes."
• "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."
• "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."