In
recreational mathematics, a polystick (or polyedge) is a
polyform with a
line segment
In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between ...
(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.
The name "polystick" seems to have been first coined by Brian R. Barwell.
The names "polytrig" and "polytwigs" 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
Spicules are any of various small needle-like anatomical structures occurring in organisms
Spicule may also refer to:
* Spicule (sponge), small skeletal elements of sea sponges
* Spicule (nematode), reproductive structures found in male nematodes ...
of
sea sponges.
There is no standard term for line segments built on other
regular tilings
This article lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces.
The Schläfli symbol describes every regular tessellation of an ''n''-sphere, Euclidean and hyperbolic spaces. A Schläf ...
, an
unstructured grid, or a simple
connected graph, but both "polynema" and "polyedge" have been proposed.
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.
Counting polyforms'', at the Solitaire Laboratory
/ref>
The set of ''n''-sticks that contain no closed loops is equivalent, with some duplications, to the set of (''n''+1)-ominos, as each vertex at the end of every line segment can be replaced with a single square of a polyomino. In general, an ''n''-stick with ''m'' loops is equivalent to a (''n''−''m''+1)-omino (as each loop means that one line segment does not add a vertex to the figure).
Diagram
References
External links
''Polysticks Puzzles & Solutions'', at Polyforms Puzzler
''Covering the Aztec Diamond with One-sided Tetrasticks'', Alfred Wassermann, University of Bayreuth, Germany
a
Math Magic
{{Polyforms
Polyforms