POLYOMINO_MULTIHEDRAL_EXAMPLE_PENT18X30
18x30 Rectangle tiled by 9 Copies of Pentominoes

POLYOMINO_MULTIHEDRAL_EXAMPLE_PENT18X30, a MATLAB program which sets up a problem in which an 18x30 rectangle is to be tiled by 9 copies of each of the 12 distinct pentominoes, and plots a solution computed by GUROBI.

Because this problem results in a large linear system to be solved, we simply set up the linear system, write it to an LP file, and have GUROBI compute a solution. The resulting solution was read by GUROBI_SOLUTION_READ and written to a file that MATLAB can access using load();

The solution to the tiling problem is then plotted.

Licensing:

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

Source Code:

• filename_inc.m numerically "increments" a file name.
• pentomino_matrix.m returns a 0/1 matrix defining a particular pentomino.
• pentomino_name.m given an index between 1 and 12, returns the corresponding name F, I, L, N, P, T, U, V, W, X, Y, or Z.
• pentomino_pack.m packs the pentominoes into an MxNx12 array.
• polyomino_condense.m, cleans up a matrix that represents a polyomino by setting all nonzero entries to 1, and removing initial and final rows and columns of zeros.
• polyomino_embed_list.m, for each possible embedding, lists the translation necessary to to apply to the polyomino.
• polyomino_embed_number.m, reports the number of ways a polyomino can be embedded in a region.
• polyomino_index.m, computes an index for each nonzero polyomino entry.
• polyomino_multihedral_example_pent18x30_define.m, defines the problem.
• polyomino_multihedral_example_pent18x30_tiling_plot.m, plots the solution.
• polyomino_multihedral_matrix.m, determines the matrix and right hand side for a polyomino multihedral problem.
• polyomino_multihedral_tiling_plot.m, is given matrices defining a region R and a set of polyominoes P, and a vector X, computed by POLYOMINO_MULTIHEDRAL, which represents a tiling of R by the polyominoes in P, and plots a representation of that tiling.
• polyomino_multihedral_variants.m, carries out reflections and rotations of all the polyominoes in a set P to determine which transformations yield distinct variants.
• polyomino_print.m, prints a polyomino.
• polyomino_transform.m, carries out reflections and rotations of a polyomino.
• timestamp.m, prints the YMDHMS date as a timestamp.

Examples and Tests:

• pent18x30_gurobi.txt, a simple text version of the GUROBI solutions, readable by load().
• pent18x30.png