Definition:Regular Star Polygon

Definition

Let $n \in \N$ be a natural number such that $n \ge 3$.

Let $m \in \N$ such that $m < n$ and such that $m$ and $n$ are coprime.

Let $\CC$ be a circle whose circumference has been divided into $n$ equal arcs by $n$ points equally spaced.

A regular star polygon is a plane figure formed by constructing a line segment joining every $m$th point of those $n$ equally spaced points.

Such a regular star polygon can be denoted $\set {n / m}$.

Examples

Regular Polygon

A regular polygon is the degenerate case of a regular star polygon where $m = 1$.

Pentagram

The pentagram is the regular star polygon identified as $\set {5 / 2}$:

A pentagram is a regular star polygon formed by the line segments connecting alternate vertices of a regular pentagon:

Also known as

A regular star polygon is also known as just a star polygon.

Also see

• Results about regular star polygons can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): polygon
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): regular star polygon
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): polygon
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): regular star polygon