recreational mathematics Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...

, a polystick (or polyedge) is a

polyform In recreational mathematics, a polyform is a plane (mathematics), plane figure or solid compound constructed by joining together identical basic polygons. The basic polygon is often (but not necessarily) a convex polygon, convex plane-filling pol ...

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 regular grid is a tessellation of ''n''-dimensional Euclidean space by congruent parallelotopes (e.g. bricks). Its opposite is irregular grid. Grids of this type appear on graph paper and may be used in finite element analysis, finite volume ...

. 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 ( ...

sea sponges Sponges, the members of the phylum Porifera (; meaning 'pore bearer'), are a basal animal clade as a sister of the diploblasts. They are multicellular organisms that have bodies full of pores and channels allowing water to circulate through ...

. 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 geometry, Euclidean, spherical geometry, spherical and hyperbolic geometry, hyperbolic spaces. The Schläfli symbol describes every regular tessellation of an ' ...

, an

unstructured grid An unstructured grid or irregular grid is a tessellation of a part of the Euclidean plane or Euclidean space by simple shapes, such as triangles or tetrahedra, in an irregular pattern. Grids of this type may be used in finite element analysis w ...

, or a simple

connected graph In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgrap ...

, 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 Vertex, vertices or vertexes may refer to: Science and technology Mathematics and computer science *Vertex (geometry), a point where two or more curves, lines, or edges meet *Vertex (computer graphics), a data structure that describes the position ...

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