Patterns which do not repeat

There are 273 non-repeating patterns.

These can be conveniently divided into three further groups.

The first group are those tilings of a rectangle by polyominoes, and two examples of which are:

Note that the first case has cyclic symmetry of order 4.

There are a total of 110 such polyominoes, being 40% of the total. There are no more choices to be made. For a tabulation of their properties, see Polyominoes.

To see all of these, you can proceed to page.

The second group are those tilings which has a spiral appearance, and two examples of which are:

There are a total of 29 such spiral tilings, being 10% of the total. There are no more choices to be made.

To see all of these, you can proceed to page.

The last group are those which are neither of the above two groups. The number of such patterns in 134, being 49% of the total. Two examples of such patterns are:

For this case, you can proceed to the next question.

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Tiling Search was created by Brian Wichmann, and is maintained by MIT Libraries, through support from the Aga Khan Documentation Center.

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