Talk:Polystick

Latest comment: 16 years ago by Nonenmac in topic Updated table

90-degree connections only?

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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)Reply

Polyedges

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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

Nonenmac (talk) 16:25, 18 July 2008 (UTC)Reply

Equivalent to:

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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

(from A019988 - Nonenmac (talk) 16:35, 18 July 2008 (UTC)Reply

Another polyedge reference

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Counting polyforms

Updated table

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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

--Nonenmac (talk) 19:37, 18 July 2008 (UTC)Reply