Here I show all the polycairinos with from 1 to 4 cells.
Two-sided polycairinos are identified under reflection as well as rotation. One-sided polycairinos are distinguished under reflection. That is, if a polycairino and its mirror image are distinct, both are counted.
| Order | Two-Sided | One-Sided |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 3 | 5 |
| 3 | 9 | 15 |
| 4 | 42 | 79 |
| 5 | 184 | 355 |
| 6 | 950 | 1 876 |
| 7 | 4 922 | 9 781 |
| 8 | 26 646 | 53 171 |
| 9 | 145 698 | 291 072 |
| 10 | 809 724 | 1 618 813 |
| 11 | 4 538 619 | 9 075 519 |
| 12 | 25 659 154 | 51 314 893 |
The figures below show the two-sided polycairinos.
Last revised 2026-04-23.