star polygon

English

A star polygon (heptagram)

Noun

star polygon (plural star polygons)

1. (geometry) A geometric figure formed by connecting, with straight lines, every vertex of a p-sided regular polygon to the qth vertex beyond it (proceeding, consistently, either clockwise or anticlockwise).

   Synonym: regular star polygon

2. Any such geometrical figure, or any of certain other types of figure of similar appearance whose general construction is not formally defined.

Usage notes

• The (modified) Schläfli symbol for a star polygon is $\{p/q\}$.
• If p and q are not coprime (i.e., if they share some factor greater than 1), the resulting figure splits the vertices into groups which are not connected, and the figure is said to be degenerate.
• If p and q are coprime, every vertex of the resulting figure is ultimately connected to every other vertex, and the figure may be said to be non-degenerate.

Hyponyms

• pentagram, star pentagon
• hexagram, star hexagon
• heptagram, star heptagon
• octagram, star octagon

Further reading

• Pentagram on Wikipedia.Wikipedia
• Stellation on Wikipedia.Wikipedia