Polytope vs Permutohedron - What's the difference?
polytope | permutohedron |
(geometry) A finite region of n -dimensional space bounded by hyperplanes; the geometrical entity represented by the general term of the infinite sequence "point, line, polygon, polyhedron, ...".
* 1964 , , On the Number of Vertices of a Convex Polytope'', ''Canadian Journal of Mathematics , Volume XVI, Number 4,
* 1998 , F. Pierrot, M. Benoit, P. Dauchez, SamoS: A Pythagorean Solution for Omnidirectional Underwater Vehicles'', Jadran Lenar I, Manfred L. Husty (editors), ''Advances in Robot Kinematics: Analysis and Control ,
* 2006 , Rekha R. Thomas, Lectures in Geometric Combinatorics ,
(mathematics) An polytope with n''-1 dimensions that is embedded in an n-dimensional space, its vertices]] formed by [[permute, permuting the coordinates of the vector (1, 2, 3, ..., ''n ).
As nouns the difference between polytope and permutohedron
is that polytope is (geometry) a finite region of n -dimensional space bounded by hyperplanes; the geometrical entity represented by the general term of the infinite sequence "point, line, polygon, polyhedron, " while permutohedron is (mathematics) an polytope with n''-1 dimensions that is embedded in an n-dimensional space, its vertices]] formed by [[permute|permuting the coordinates of the vector (1, 2, 3, , ''n ).polytope
English
(wikipedia polytope)Noun
(en noun)page 701,
- As is well known, the theory of linear inequalities is closely related to the study of convex polytopes .
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.
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 .