Polyhings

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Polyhings are formed from regular hexagons joined edge-to-edge or corner-to-corner. They form a subset of the polymings of six times the order. Connecting bridges may be added to the cornerwise joints to create a solid set of pieces without affecting their combinatorial properties, since the pieces cannot cross unlike many other polymings. However, bridges will affect the visual symmetry of some patterns.

 Monohing - 1 (1 tile)

       

 Dihings - 2 (4 tiles)

     
1 2      

 Trihings - 8 (24 tiles)

1 2 3 4 5
   
6 7 8    

 

 Tetrahings - 45 (180 tiles)

1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
16 17 18 19 20
21 22 23 24 25
26 27 28 29 30
31 32 33 34 35
36 37 38 39 40
41 42 43 44 45

  For higher orders of polyhings, the number of pieces is as follows (totals courtesy of George Sicherman):

  Pentahings - 322

  Hexahings  - 2,859

  Heptahings - 26,675

  Octahings   - 259,756

 

Puzzles using Polyhings

 

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