Polycairos are formed from any of a family of pentagons containing two right angles with one angle between them. To create a cairo, first draw a square. Make an identical copy, placing one corner at the centre of the first square. Now rotate the second square around this corner - the area of overlap is half of the cairo. Polycairos are confined to a grid in the form of the Cairo Tessellation, which gives the pieces their name. Although equilateral polycairos can be made, for most puzzles the exact form of the cairo generator does not matter.
Monocairo - 1 (1 tiles)
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Dicairos - 2 (4 tiles)
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Tricairos - 5 (15 tiles)
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| 1 | 2 | 3 | 4 | 5 |
Tetracairos - 17 (68 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 | 14 | 15 |
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| 16 | 17 |
For higher orders of Polycairos, the number of pieces is as follows:
Pentacairos - 55
Hexacairos - 206
Heptacairos - 781
Octacairos - 3099
Enneacairos - 12421
Decacairos - 50725