Polywaves are formed from kite-shaped pieces consisting of an equilateral triangle and a tan, or quarter-square. The pieces are constrained to the grid shown below, with the pieces resembling polyominoes with wavy edges.
Monowave - 1 (1 tile)
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Diwaves - 2 (4 tiles)
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Triwaves - 4 (12 tiles)
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| 1 | 2 | 3 | 4 |
Tetrawaves - 13 (52 tiles)
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| 1 | 2 | 3 | 4 | 5 |
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| 6 | 7 | 8 | 9 | 10 |
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| 11 | 12 | 13 |
Pentawaves - 34 (170 tiles)
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| 1 | 2 | 3 | 4 | 5 | 6 |
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| 7 | 8 | 9 | 10 | 11 | 12 |
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| 13 | 14 | 15 | 16 | 17 | 18 |
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| 19 | 20 | 21 | 22 | 23 | 24 |
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| 25 | 26 | 27 | 28 | 29 | 30 |
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| 31 | 32 | 33 | 34 |
For higher orders of Polywaves, the number of pieces is as follows:
Hexawaves - 120
Heptawaves - 388
Octawaves - 1404