# polytope

suomi-englanti sanakirja## polytope englanniksi

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, ...". geometry

1964, Klee|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'', 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.