Face configuration

Face configuration

In geometry, a "face configuration" is notational description of a face-transitive polyhedron. It represents a sequential count of the number of faces that exist at each vertex around a face.

There is no single standard accepted representation, but one common notation prefixes the description with a "V" and separates the vertices by a period (".") or a comma (",").

For example, V3.4.3.4 represents the rhombic dodecahedron which is face-transitive: every face is a rhombus, and alternating vertices of the rhombus contain 3 or 4 faces each.

Another form of this notation, used in "Tilings and Patterns", has brackets around the symbol, for instance [3.4.3.4] .

Face-transitive polyhedra are generally the polyhedral duals of the vertex-transitive polyhedra, which are described by a parallel vertex configuration notation. That notation omits the "V" prefix and represents sequentially the number of edges of the faces around a vertex. For example, 3.4.3.4 is the cuboctahedron with alternating triangular and square faces around each vertex. Polyhedra have the same representation in face configuration notation (with the addition of the "V") that their duals have in vertex configuration notation. The rhombic dodecahedron (V3.4.3.4) and the cubocahedron (3.4.3.4) above are dual polyhedra.

See also

* Platonic solids: five regular polyhedra that are either self-dual or whose dual is another Platonic solid.
* Catalan solids: thirteen polyhedra that are dual to the Archimedean solids
* Bipyramids: an infinite set of duals of prisms
* Trapezohedrons: an infinite set of duals of antiprisms
* List of uniform planar tilings

References

*
* Branko Grünbaum and G. C. Shephard "Tilings and Patterns". New York: W. H. Freeman & Co., 1987. ISBN 0-7167-1193-1.


Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • Configuration — Con*fig u*ra tion, n. [L. configuratio.] 1. Form, as depending on the relative disposition of the parts of a thing; shape; figure. [1913 Webster] It is the variety of configurations [of the mouth] . . . which gives birth and origin to the several …   The Collaborative International Dictionary of English

  • Configuration d'aile — Réplique du Fokker Dr.I, triplan piloté par le Baron rouge lors de la Première Guerre mondiale. Depuis les débuts de l aviation, de nombreuses configurations d aile ont été imaginées pour permettre aux « plus lourds que l air » – d… …   Wikipédia en Français

  • configuration — noun a) Form, as depending on the relative disposition of the parts of a things shape; figure; form factor. b) Relative position or aspect of the planets; the face of the horoscope, according to the relative positions of the planets at any time …   Wiktionary

  • Vertex configuration — In polyhedral geometry a vertex configuration is a short hand notation for representing a polyhedron vertex figure as the sequence of faces around a vertex. For uniform polyhedra there is only one vertex type and therefore the vertex… …   Wikipedia

  • Möbius configuration — Example of Möbius configuration; the face planes of red tetrahedron are shown on the top of the image; the blue one on the bottom. The vertex coordinates of the red tetrahedron are: (0,0,0),(0,0,1),(0,1,0),(1,0,0). The vertex coordinates of the… …   Wikipedia

  • Pile ou face — Pour les articles homonymes, voir Pile ou face (homonymie). Lancer d une pièce. Le pile ou face est un jeu de hasard se jouant avec une pièce de monnaie. Le principe du jeu e …   Wikipédia en Français

  • Software configuration management — In software engineering, software configuration management (SCM) is the task of tracking and controlling changes in the software. Configuration management practices include revision control and the establishment of baselines.SCM concerns itself… …   Wikipedia

  • X-Face — An X Face is a small bitmap (48 × 48 pixels, black and white) image which is added to a Usenet posting or e mail message, typically showing a picture of the author s face. The image data is included in the posting as encoded text, and attached… …   Wikipedia

  • Bisected hexagonal tiling — Type Dual semiregular tiling Faces 30 60 90 triangle Face configuration V4.6.12 …   Wikipedia

  • List of uniform tilings — This table shows the 11 convex uniform tilings of the Euclidean plane, and their dual tilings.There are three regular, and eight semiregular, tilings in the plane. The semiregular tilings form new tilings from their duals, each made from one type …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”