polyiamonds


polyiamonds, a MATLAB code which considers polyiamonds, simple connected shapes constructed from equilateral triangles connected edgewise.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

polyiamonds is available in a MATLAB version and an Octave version.

Related Data and Programs:

boundary_word_square, a MATLAB code which describes the outline of an object on a grid of squares, using a string of symbols that represent the sequence of steps tracing out the boundary.

boundary_word_triangle, a MATLAB code which describes the outline of an object on a grid of triangles, using a string of symbols that represent the sequence of steps tracing out the boundary.

eternity, a MATLAB code which considers the eternity puzzle, which considers an irregular dodecagon shape that is to be tiled by 209 distinct pieces, each formed by 36 contiguous 30-60-90 triangles, known as polydrafters.

pariomino, a MATLAB code which considers pariominoes, which are polyominoes with a checkerboard parity, and the determination of tilings of a region using a specific set of pariominoes.

polyiamonds_test

polyominoes, a MATLAB code which defines, solves, and plots a variety of polyomino tiling problems, which are solved by a direct algebraic approach involving the reduced row echelon form (RREF) of a specific matrix, instead of the more typical brute-force or backtracking methods.

Reference:

  1. Martin Gardner,
    Mathematical Games: On Polyiamonds: Shapes That are Made Out of Equilateral Triangles, Scientific American,
    Volume 211, December 1964.
  2. Marcus Garvie, John Burkardt,
    A new mathematical model for tiling finite regions of the plane with polyominoes,
    Contributions to Discrete Mathematics,
    Volume 15, Number 2, July 2020.
  3. Solomon Golomb,
    Polyominoes: Puzzles, Patterns, Problems, and Packings,
    Princeton University Press, 1996,
    ISBN: 9780691024448
  4. T H O'Beirne,
    Pentominoes and Hexiamonds,
    New Scientist,
    Volume 12, pages 379-380, 1961.
  5. Torbijn,
    Polyiamonds,
    Journal of Recreational Mathematics,
    Volume 2, pages 216-227, 1969.

Source code:


Last revised on 11 November 2020.