polytope en · NOUN
Pronunciation
- /ˈpɑliˌtoʊp/ (US)
- (US) audio
- /ˈpɒliːˌtəʊp/ (UK)
- /ˈpɒlɪˌtəʊp/ (UK)
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”).
Meanings
-
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.
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: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: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:
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| polytopes | Number=Plur | lexicographic |
Deriveds
Hanner polytope · 1-polytope · matroid polytope · polytopal · cyclic polytope · 5-polytope · n-polytope · Birkhoff polytope · cross-polytope · 2-polytope · uniform polytope · integral polytope · 4-polytope · pentagonal polytope · random polytope · convex polytope · zonotope · parallelotope · 0-polytope · regular polytope · 3-polytope · chiral polytope · abstract polytope
Hyponyms
simplex · hypercube · polygon (classes of a given dimension) · tesseract · polyhedron (classes of a given dimension) · polychoron (classes of a given dimension)
Relateds
Translations (20)
pl wielokomórka (geometric shape) · pl politop (geometric shape) · fa چندبر (geometric shape) · ca polítop (geometric shape) · eo hiperpluredro (geometric shape) · de Polytop (geometric shape) · ja ポリトープ (geometric shape) · uk політо́п (geometric shape) · ru полито́п (geometric shape) · cmn 多胞形 (geometric shape) · el πολύτοπο (geometric shape) · sv polytop (geometric shape) · pt politopo (geometric shape) · ko 다포체 (geometric shape) · es politopo (geometric shape) · fr polytope (geometric shape) · it politopo (geometric shape) · ja 超多面体 (geometric shape) · pl wielotop (geometric shape) · hu politóp (geometric shape)