Compute Distinct Polyomino Variants

POLYOMINO_MULTIHEDRAL_VARIANTS, a MATLAB program which computes the distinct variants of one or more polyominoes under reflection and 90 degree rotations.

A polyomino P is a shape formed by connecting unit squares. It can be described by a rectangular binary matrix. The matrix is assumed to be "top-left tight", that is, there must be a 1 in the first row, and in the first column of the matrix, but there may be trailing rows and columns of zeroes.

A polyomino can be rotated by 90, 180, or 270 degrees, and it can be reflected. There are 8 combinations of these transformations possible, so there are 8 variations of a given polyomino. However, because of symmetry, there may be 1, 2, 4, or 8 distinct variations.

This program accepts the binary matrices describing one or more polyominoes, generates all the possible variations, and returns those which are distinct.


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


polyomino_multihedral_variants is available in a MATLAB version.

Related Data and Programs:


Source Code:

Last revised on 06 March 2019.