Polystick

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.

The following diagram shows the 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