90-degree connections only?
Having never heard of a polysick, I did a Google search and found little except for information on an adhesive product and numerous Wikipedia clone articles identical to this and the polyform article which links here. The only applicable outside article that I did find was http://puzzler.sourceforge.net/docs/polysticks.html#polysticks-of-order-1-through-4, which infers (based on the picture of a solution) that polysticks can be joined, not only at 90 degrees, but also at 0 degrees. This article just mentions the 90-degree connections, but allowing both 0 and 90 makes more sense to me. Nonenmac (talk) 01:01, 18 July 2008 (UTC)
Polyedges
From: http://puzzler.sourceforge.net/docs/FAQ.html
Polysticks (a.k.a. "polyedges"; A019988):
| Sticks | Name | Polysticks | One-Sided |
|---|---|---|---|
| 1 | monostick | 1 | 1 |
| 2 | distick | 2 | 2 |
| 3 | tristick | 5 | 7 |
| 4 | tetrastick | 16 | 25 |
| 5 | pentastick | 55 | 99 |
Equivalent to:
Number of ways of embedding a connected graph with n edges in the square lattice:
1, 2, 5, 16, 55, 222, 950, 4265, 19591, 91678, 434005, 2073783, 9979772, 48315186, 235088794, 1148891118, 5636168859
Another polyedge reference
Updated table
| Number of Sticks | Name of Polystick | Number of Free Polysticks | Number of One-Sided Polysticks |
|---|---|---|---|
| 1 | monostick | 1 | 1 |
| 2 | distick | 2 | 2 |
| 3 | tristick | 5 | 7 |
| 4 | tetrastick | 16 | 25 |
| 5 | pentastick | 55 | 99 |
| 6 | hexastick | 222 | |
| 7 | heptastick | 950 | |
| 8 | octastick | 4265 |