Polytwigs can be regarded as unit lines confined to the regular hexagonal grid. Physical pieces can be constructed for the polytwigs.
The polytwigs can be emulated on a regular hexagonal grid, with some of the cells excluded. Such a grid is shown below with excluded cells in black, and the same tetratwig as above highlighted in blue. Each polyhex that fits within this grid has a polytwig equivalent.
Monotwig - 1 (1 line)
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Ditwigs - 1 (2 lines)
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| 1 |
Tritwigs - 3 (9 lines)
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| 1 | 2 | 3 |
Tetratwigs - 4 (16 lines)
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| 1 | 2 | 3 | 4 |
Pentatwigs - 12 (60 lines)
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| 1 | 2 | 3 | 4 | 5 | 6 |
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| 7 | 8 | 9 | 10 | 11 | 12 |
Hexatwigs - 27 (162 lines)
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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 |
For higher orders of polytwigs, the number of pieces is as follows:
Heptatwigs - 78
Octatwigs - 208
Enneatwigs - 635
Decatwigs - 1859
Puzzles using Tetra- and Pentatwigs