Fațetă (geometrie)

În geometrie, o fațetă este o componentă a unui poliedru, politop sau a unei structuri geometrice înrudite, având, în general, o dimensiune mai puțin decât structura în sine.

  • În geometria tridimensională, o fațetă a unui poliedru este orice poligon ale cărui colțuri sunt vârfurile poliedrului, și care nu este o față.[1][2] Fațetarea unui poliedru înseamnă a găsi și a uni astfel de fațete pentru a forma fețele unui poliedru nou; acesta este procesul invers al stelării și poate fi aplicat și politopurilor cu dimensiuni superioare.[3]
  • În combinatorica poliedrică⁠(d) și în teoria generală a politopurilor, o fațetă a unui politop de dimensiunea n este o față care are dimensiunea (n − 1). În geometria tridimensională, ele sunt adesea numite „fețe”, fără alt calificativ.[4]
  • O fațetă a unui complex simplicial este un simplex maximal, adică un simplex care nu este o față a unui alt simplex al complexului.[5] În cazul (complexelor pe margini ale) simplexurilor, aceasta coincide cu semnificația din combinatorica poliedrică.

Note

  1. ^ en Bridge, N.J. Facetting the dodecahedron, Acta crystallographica A30 (1974), pp. 548–552.
  2. ^ en Inchbald, G. Facetting diagrams, The mathematical gazette, 90 (2006), pp. 253–261.
  3. ^ en Coxeter, H.S.M. (), Regular Polytopes, Dover, p. 95 .
  4. ^ en Matoušek, Jiří (), Lectures in Discrete Geometry, Graduate Texts in Mathematics, 212, Springer, 5.3 Faces of a Convex Polytope, p. 86, ISBN 9780387953748 .
  5. ^ en De Loera, Jesús A.; Rambau, Jörg; Santos, Francisco (), Triangulations: Structures for Algorithms and Applications, Algorithms and Computation in Mathematics, 25, Springer, p. 493, ISBN 9783642129711 .

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