In recreational mathematics, a polystick (or polyedge) is a polyform with a line segment (a 'stick') as the basic shape. A polystick is a connected set of segments in a regular grid. A square polystick is a connected subset of a regular square grid. A triangular polystick is a connected subset of a regular triangular grid. Polysticks are classified according to how many line segments they contain.[1]
The name "polystick" seems to have been first coined by Brian R. Barwell.[2]
The names "polytrig"[3] and "polytwigs"[4] has been proposed by David Goodger to simplify the phrases "triangular-grid polysticks" and "hexagonal-grid polysticks," respectively. Colin F. Brown has used an earlier term "polycules" for the hexagonal-grid polysticks due to their appearance resembling the spicules of sea sponges.[5]
There is no standard term for line segments built on other regular tilings, an unstructured grid, or a simple connected graph, but both "polynema" and "polyedge" have been proposed.[6]
When reflections are considered distinct we have the one-sided polysticks. When rotations and reflections are not considered to be distinct shapes, we have the free polysticks. Thus, for example, there are 7 one-sided square tristicks because two of the five shapes have left and right versions.[7] [8]
| align=center colspan=4 | Square Polysticks | |||
| Sticks | Name | Free | One-Sided | |
|---|---|---|---|---|
| 1 | monostick | 1 | 1 | |
| 2 | distick | 2 | 2 | |
| 3 | tristick | 5 | 7 | |
| 4 | tetrastick | 16 | 25 | |
| 5 | pentastick | 55 | 99 | |
| 6 | hexastick | 222 | 416 | |
| 7 | heptastick | 950 | 1854 |
| align=center colspan=4 | Hexagonal Polysticks | |||
| Sticks | Name | Free | One-Sided | |
|---|---|---|---|---|
| 1 | monotwig | 1 | 1 | |
| 2 | ditwig | 1 | 1 | |
| 3 | tritwigs | 3 | 4 | |
| 4 | tetratwigs | 4 | 6 | |
| 5 | pentatwigs | 12 | 19 | |
| 6 | hexatwigs | 27 | 49 | |
| 7 | heptatwigs | 78 | 143 |
| align=center colspan=4 | Triangular Polysticks | |||
| Sticks | Name | Free | One-Sided | |
|---|---|---|---|---|
| 1 | monostick | 1 | 1 | |
| 2 | distick | 3 | 3 | |
| 3 | tristick | 12 | 19 | |
| 4 | tetrastick | 60 | 104 | |
| 5 | pentastick | 375 | 719 | |
| 6 | hexastick | 2613 | 5123 | |
| 7 | heptastick | 19074 | 37936 |