Polyhex (mathematics)

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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, … (sequence A000228 in OEIS); the number of free polyhexes with holes is given by OEISA038144; the number of free polyhexes without holes is given by OEISA018190; the number of fixed polyhexes is given by OEISA001207; the number of one-sided polyhexes is given by OEISA006535.[1][2]

The Monohex: The Monohex
The Dihex: The Dihex
The 3 Trihexes: The 3 Trihexes
The 7 Tetrahexes: The 7 Tetrahexes
The 22 Pentahexes: The 22 Pentahexes
The 82 Hexahexes: The 82 Hexahexes

See also[edit]

References[edit]

  1. ^ Wolfram Mathworld: Polyhex
  2. ^ Glenn C. Rhoads, Planar tilings by polyominoes, polyhexes, and polyiamonds, Journal of Computational and Applied Mathematics 174 (2005), No. 2, pp 329–353