different between polytope vs polytopal

English

Etymology

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

Noun

polytope (plural polytopes)

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, ...".
   • 1964, 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.

Related terms

• polytopic

Hyponyms

• (geometrical figure): polygon (2d figure), polyhedron (3d figure), polychoron (4d figure), hypercube (generalised cube), simplex (generalised tetrahedron), tesseract (4d cube)

Translations

References

French

Noun

polytope m (plural polytopes)

1. polytope

English

Etymology

polytope +? -al

Adjective

polytopal (comparative more polytopal, superlative most polytopal)

1. (mathematics) Of or pertaining to polytopes.
2. (chemistry) Describing any rearrangement reaction involving atoms or groups at the vertices of a polyhedron.