Polystick


In recreational mathematics, a polystick is a polyform with a line segment 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.
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.
The set of n-sticks that contain no closed loops is equivalent, with some duplications, to the set of -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 -omino.

Diagram