boundary_word_right

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

A shape constructed from edgewise connected isoceles right triangles is called a polyabolo, or sometimes a polytan.

A version of the famous "T" puzzle uses 4 polyabolo tiles to cover a grid shaped like a "T".

Licensing:

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

Languages:

boundary_word_right is available in a MATLAB version.

Related Data and Programs:

boundary_word_right_test

boundary_word_drafter, a MATLAB code which describes the outline of an object on a grid of drafters, or 30-60-90 triangles, using a string of symbols that represent the sequence of steps tracing out the boundary.

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

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

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.

polyiamonds, a MATLAB code which works with polyiamonds, simple shapes constructed by edgewise connections of congruent equilateral triangles.

t_puzzle_gui, a MATLAB code which sets up a graphical user interface for the T puzzle.

Reference:

1. Erich Friedman,
   Math Magic, Problem of the month, September 2004,
   https://erich-friedman.github.io/mathmagic/0904.html.
2. Martin Gardner,
   Mathematical Games: The polyhex and the polyabolo, polygonal jigsaw puzzle pieces, Scientific American,
   Volume 216, June 1967, pages 124-132.
3. Martin Gardner,
   Mathematical Games: Advertising premiums to beguile the mind: classics by Sam Loyd, master puzzle poser,
   Scientific American,
   Volume 225, Number 5, pages 114-121, November 1971.
4. 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.
5. Solomon Golomb,
   Polyominoes: Puzzles, Patterns, Problems, and Packings,
   Princeton University Press, 1996,
   ISBN: 9780691024448
6. Thomas O'Beirne,
   Pentominoes and Hexiamonds,
   New Scientist,
   Volume 12, pages 379-380, 1961.

Source code:

• boolean_to_string.m, given a boolean value, returns the character vector 'True' or 'False'.
• ch_wrap.m, forces a character to lie between given limits by wrapping.
• chvec_lt.m, is TRUE if c1
• gort_word.m, returns the boundary word of the Gort polyabolo.
• grid_plot.m, plots an isoceles right triangle grid.
• heart_word.m, returns the boundary word of the heart polyabolo, which can be exactly covered by the 14 tetrabolos.
• i4_wrap.m, forces an integer to lie between given limits by wrapping.
• ijk_fill.m, given (i,j,k) polyabolo coordinates, plots a filled triangle on the current figure.
• ijk_to_xy.m, given (i,j,k) polyabolo coordinates, returns the (x,y) Cartesian point coordinates of the nodes that are vertices.
• is_octave.m, is TRUE if Octave is executing.
• s_escape_tex.m, de-escapes TeX escape sequences.
• s_substitute.m, substitutes characters in a string.
• tee_word.m, returns the boundary word of the T polyabolo.
• tetrabolo_name.m, given an index of a tetrabolo, returns the corresponding Gardner and Friedman names.
• tetrabolo_word.m, given an index of a tetrabolo, returns the corresponding boundary word and base point.
• tiny_word.m, returns the boundary word of the tiny polyabolo.
• vertex_contains_ijk.m, given the vertex list of a polyabolo, determines if it contains an IJK triangle.
• vertex_contains_point.m, given the vertex list of a polyabolo, determines if a point is contained inside.
• vertex_plot.m, given the vertex list of a polyabolo, produces a plot.
• vertex_to_triangle.m, given the vertex list of a polyabolo, produces the corresponding triangle list.
• word_plot.m, given the boundary word of a polyabolo, creates a plot.
• word_print.m, given the boundary word of a polyabolo, prints it.
• word_range.m, given the boundary word of a polyabolo, returns its range in the I and J directions.
• word_reflect.m, given the boundary word of a polyabolo, returns the boundary word of the polyabolo reflected up and down.
• word_representative.m, returns the representative for a boundary word, the lexically first member of the equivalence class.
• word_rotate.m, returns the boundary word for a rotated object.
• word_to_triangle.m, given the boundary word of a polyabolo, converts it to a triangle list.
• word_to_vertex.m, given the boundary word of a polyabolo, converts it to a vertex list.