different between polytope vs polytype

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

poly- +? type

Noun

polytype (plural polytypes)

1. Any of the types involved in polytypism.

2. A cast, or facsimile copy, of an engraved block, matter in type, etc.
   • 1825, Thomas Curson Hansard, Typographia, an Historical Sketch of the Origin and Progress of the Art of Printing

     Towards the end of the eighteenth century , Professor Wilson of Glasgow , being engaged in a series of experiments for making etchings upon glass with fluoric acid for the purposes of art , thought it possible to make polytypes of glass from engraved copperplates

3. (computing theory) In the Hindley–Milner type system, a data type containing variables bound by one or more ? (for-all) quantifiers.

   Coordinate term: monotype

Verb

polytype (third-person singular simple present polytypes, present participle polytyping, simple past and past participle polytyped)

1. (transitive) To produce a polytype of.

   to polytype an engraving

French

Pronunciation

• Homophones: polytypent, polytypes

Verb

polytype

1. first-person singular present indicative of polytyper
2. third-person singular present indicative of polytyper
3. first-person singular present subjunctive of polytyper
4. third-person singular present subjunctive of polytyper
5. second-person singular imperative of polytyper