Pentomino

The 12 pentominoes can form 18 different shapes, with 6 of them (the chiral pentominoes) being mirrored.

Derived from the Greek word for '5', and "domino", a pentomino (or 5-omino) is a polyomino of order 5; that is, a polygon in the plane made of 5 equal-sized squares connected edge to edge. When rotations and reflections are not considered to be distinct shapes, there are 12 different free pentominoes. When reflections are considered distinct, there are 18 one-sided pentominoes. When rotations are also considered distinct, there are 63 fixed pentominoes.

Pentomino tiling puzzles and games are popular in recreational mathematics.[1] Usually, video games such as Tetris imitations and Rampart consider mirror reflections to be distinct, and thus use the full set of 18 one-sided pentominoes. (Tetris itself uses 4-square shapes.)

Each of the twelve pentominoes satisfies the Conway criterion; hence, every pentomino is capable of tiling the plane.[2] Each chiral pentomino can tile the plane without being reflected.[3]

  1. ^ "Eric Harshbarger - Pentominoes".
  2. ^ Rhoads, Glenn C. (2003). Planar Tilings and the Search for an Aperiodic Prototile. PhD dissertation, Rutgers University.
  3. ^ Gardner, Martin (August 1975). "More about tiling the plane: the possibilities of polyominoes, polyiamonds and polyhexes". Scientific American. 233 (2): 112–115. doi:10.1038/scientificamerican0775-112.