Polytrigs can be regarded as unit lines confined to the regular triangular grid. I use the convention that polylines are allowed to cross each other, whilst polytrigs cannot. Physical pieces can be constructed for the polytrigs but there will be gaps left at some nexuses.
Monotrig - 1 (1 line)
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Ditrigs - 3 (6 lines)
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| 1 | 2 | 3 |
Tritrigs - 12 (36 lines)
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| 1 | 2 | 3 | 4 | 5 | 6 |
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| 7 | 8 | 9 | 10 | 11 | 12 |
For higher orders of polytrigs, the number of pieces is as follows:
Tetratrigs - 60
Pentatrigs - 375
Hexatrigs - 2613
Heptatrigs - 19074
Octatrigs - 14366