Polyhex (mathematics)

Polyhex (mathematics)

In recreational mathematics, a polyhex is a polyform with a regular hexagon (or 'hex' for short) as the base form.

As with polyominoes, polyhexes may be enumerated as "free" polyhexes (where rotations and reflections count as the same shape), "fixed" polyhexes (where different orientations count as distinct) and "one-sided" polyhexes (where mirror images count as distinct but rotations count as identical). They may also be distinguished according to whether they may contain holes. The number of free n-hexes for n = 1, 2, 3, … is 1, 1, 3, 7, 22, 82, 333, 1448, … OEIS|id=A000228; the number of free polyhexes with holes is given by OEIS2C|id=A038144; the number of free polyhexes without holes is given by OEIS2C|id=A018190; the number of fixed polyhexes is given by OEIS2C|id=A001207; the number of one-sided polyhexes is given by OEIS2C|id=A006535.

ee also

*Tessellation
*Percolation theory
*Polyiamond - tilings with equilateral triangles
*Polyomino - tilings with squares
*Polycyclic aromatic hydrocarbon - hydrocarbons whose structure is based on polyhexes


Wikimedia Foundation. 2010.

Игры ⚽ Нужна курсовая?

Look at other dictionaries:

  • Polyhex — or polyhex can mean: * Polyhex (mathematics), a mathematical shape * Polyhex (Transformers), a fictional city in the Transformers stories …   Wikipedia

  • List of mathematics articles (P) — NOTOC P P = NP problem P adic analysis P adic number P adic order P compact group P group P² irreducible P Laplacian P matrix P rep P value P vector P y method Pacific Journal of Mathematics Package merge algorithm Packed storage matrix Packing… …   Wikipedia

  • Domino (mathematics) — The single free domino In mathematics, a domino is a polyomino of order 2, that is, a polygon in the plane made of two equal sized squares connected edge to edge.[1] When rotations and reflections are not considered to be distinct shapes, there… …   Wikipedia

  • Polyomino — The 18 one sided pentominoes, including 6 mirrored pairs …   Wikipedia

  • Nonomino — A nonomino (enneomino or 9 omino) is a polyomino of order 9, that is, a polygon in the plane made of 9 equal sized squares connected edge to edge.[1] The name of this type of figure is formed with the prefix non(a) . When rotations and… …   Wikipedia

  • Polycube — In recreational mathematics, a polycube is a polyform with a cube as the base form. Consequently they are the three dimensional analogues of the planar polyominos. The Soma cube and the Bedlam cube are examples of packing problems based on… …   Wikipedia

  • Octomino — The 369 free octominoes An octomino (or 8 omino) is a polyomino of order 8, that is, a polygon in the plane made of 8 equal sized squares connected edge to edge.[1] The name of this type of figure is formed with the prefix …   Wikipedia

Share the article and excerpts

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