Polycairos

All images © Abaroth. Permission is given to reproduce for non-profit purposes only.

Home   Historic Sites   Models   Heraldry   Puzzles   Garden   Links

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)

       

 Dicairos - 2 (4 tiles)

     

 Tricairos - 5 (15 tiles)

1 2 3 4 5

 Tetracairos - 17 (68 tiles)

1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
     
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

 

 

Home   Historic Sites   Models   Heraldry   Puzzles   Garden   Links

Contact me with suggestions, comments or questions.

free hit counter