Faceting

In Geometry, the faceting is the process of removal of parts of a Polygone, a Polyèdre or a Polytope, without creating new tops.

Faceting is the reciprocal one or the process Dual of the Stellation. For each stellation of some polytope convex, there exists a dual faceting of a dual Polytope.

History

The Facettage was not studied as extensively as the Stellation.

In 1858, Bertrand derived the spangled polyhedral (solid of Kepler-Poinsot) by faceting the Icosaèdre and the Dodécaèdre Régulier S and convex S.

In 1974, Bridge enumerated the most direct facetings of the regular polyhedral , including those of the Dodécaèdre.

In 2006, Inchbald descrivit the basic theory of the diagram of faceting for the polyhedrons. For a certain top, the diagram shows all the possible edges and the facets (new faces) which can be used to form facetings of the original hull. It is the Dual diagram of stellation of the dual Polyèdre, which shows all the possible edges and the tops for a certain plane face of the original core.

References

  • Bertrand, J. Note on the theory of the regular polyhedrons, Reports of the meetings of the Academy of Science , 46 (1858), pp. 79-82.
  • Bridge, N.J. Facetting the dodecahedron, Acta crystallographica A30 (1974), pp. 548-552.
  • Inchbald, G. Facetting diagrams, The mathematical gazette , 90 (2006), pp. 253-261.

Random links:Basingstoke | Insurance on death | The Unicorn (cartoon) | Adjective of color | January 1430 | Formation_à_haute_intensité_d'intervalle