Polystick
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In recreational mathematics, a polystick (or polyedge) is a polyform with a line segment (a 'stick') as the basic shape. Polysticks result when identical line segments are joined together end-to-end at 0° or 90° angles.
The possible different polysticks, not including rotations and reflections, include:
- 1 monostick,
- 2 disticks,
- 5 tristicks, and
- 16 tetrasticks.
| 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 |
The following diagram shows the (free) polysticks of sizes 1 through 4, including the 1 monostick (red), 2 disticks (green), 5 tristicks (blue), and 16 tetrasticks (black).
References
- Polysticks Puzzles & Solutions, at Polyforms Puzzler
- Counting polyforms, at the Solitaire Laboratory
- "Sloane's A019988 : Number of ways of embedding a connected graph with n edges in the square lattice", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- Covering the Aztec Diamond with One-sided Tetrasticks, Alfred Wassermann, University of Bayreuth, Germany
- Polypolylines, at Math Magic
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