different between polytope vs tesseract

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

From tessara- (“four-”) +? Ancient Greek ????? (aktís, “ray”).

Noun

tesseract (plural tesseracts)

1. (mathematics) The four-dimensional analogue of a cube; a 4D polytope bounded by eight cubes (in the same way a cube is bounded by six squares).
2. (science fiction) Any of various fictional mechanisms that explain extradimensional, superluminal, or time travel outside the geometry of the physical universe.

Synonyms

• (analogue of a cube): four-dimensional hypercube, 4-cube, 8-cell, octachoron, tetracube

Hypernyms

• hypercube, polytope

Derived terms

• tesseractic

Translations

See also

• tesseract on Wikipedia.Wikipedia
• Mathworld article on the tesseract

Anagrams

• rascettes