Polygems are formed from 1/3rd of a hexagon divided by lines from opposing midpoints. They are a subset of the polykites of twice the order.
Monogem - 1 (1 tile)
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Digems - 4 (8 tiles)
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| 1 | 2 | 3 | 4 |
Trigems - 15 (45 tiles)
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| 1 | 2 | 3 | 4 | 5 |
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| 6 | 7 | 8 | 9 | 10 |
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| 11 | 12 | 13 | 14 | 15 |
For higher orders of polygems, the number of pieces is as follows:
Tetragems - 78
Pentagems - 450
Hexagems - 2876
Heptagems - 18792