parallelogram vertics on star
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In geometry, a star polygon is a type of non-convex polygon. Only the regular star polygons have been studied in any depth; star polygons in general appear not to have been formally defined, however certain notable ones can arise through truncation operations on regular simple and star polygons.
Branko Grünbaum identified two primary definitions used by Johannes Kepler, one being the regular star polygons with intersecting edges that don't generate new vertices, and the second being simple isotoxal concave polygons.
The first usage is included in polygrams which includes polygons like the pentagram but also compound figures like the hexagram
A regular star pentagon, {5/2}, has five corner vertices and intersecting edges, while concave decagon, |5/2|, has ten edges and two sets of five vertices. The first are used in definitions of star polyhedra and star uniform tilings, while the second are sometimes used in planar tilings.
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