Unit line segments of the hexagonal (honeycomb) lattice joined end to end; only three segments meet at each vertex.
The 12 free pentatwigs.
| Figure | Order | Free | One-sided | Fixed | Verified |
|---|---|---|---|---|---|
| monotwig | 1 | 1 | 1 | 3 | ✓ 14/14 |
| ditwig | 2 | 1 | 1 | 6 | ✓ 14/14 |
| tritwig | 3 | 3 | 4 | 14 | ✓ 14/14 |
| tetratwig | 4 | 4 | 6 | 36 | ✓ 14/14 |
| pentatwig | 5 | 12 | 19 | 99 | ✓ 14/14 |
| hexatwig | 6 | 27 | 49 | 281 | ✓ 14/14 |
| heptatwig | 7 | 78 | 143 | 816 | ✓ 12/12 |