nLab center of a regular polygon

Definition

Let $\mathcal{P}$ be a regular polygon in an Euclidean space $\mathbb{R}^n$, and let $\mathcal{E}$ be the subset of all points in $\mathbb{R}^n$ that is equidistant from all vertices of the regular polygon.

The center of the regular polygon $\mathcal{P}$ is the unique point $p \in \mathcal{E}$ such that for any other point $q \in \mathcal{E}$, the distance from $p$ to a vertex of the polygon is less than or equal to the distance from $q$ to the same vertex of the polygon. The distance from the center of the regular polygon to a vertex of a regular polygon is called the circumradius of the regular polygon.

See also

• regular polygon

References

• Wikipedia, Regular polygon