Polystick

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]

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.[2][3]

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

Triangular Polysticks

Sticks Name Free
1 monostick 1
2 distick 3
3 tristick 12
4 tetrastick 60
5 pentastick 375
6 hexastick 2613
7 heptastick 19074

The following diagram shows the (free) square polysticks of sizes 1 through 4, including the 1 monostick (red), 2 disticks (green), 5 tristicks (blue), and 16 tetrasticks (black).

References

  1. ↑ "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.
  2. ↑ Weisstein, Eric W. "Polystick." From MathWorld
  3. ↑ Counting polyforms, at the Solitaire Laboratory

External links

This article is issued from Wikipedia - version of the 8/10/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.