Regular polygon

A polygon whose sides are all equal in length and whose interior angles are all equal in measure. Its vertices lie on a common circle, and its center is equally distant from each vertex.

Polygon: A closed plane figure formed from a finite sequence of straight line segments. A regular polygon is the equal-sided, equal-angled special case of this broader figure.
Exterior angle: An angle between one side of a polygon and the extension of an adjacent side. Each regular polygon’s exterior angle is 360° divided by its number of sides.
Tessellation: A covering of a plane with shapes that fit together without gaps or overlaps. Equilateral triangles, squares, and regular hexagons each tile the plane by themselves.
Equilateral polygon: A polygon whose sides all have equal length, without requiring equal interior angles. Equal sides alone do not make a polygon regular.
Interior angle: An angle formed inside a polygon by two adjacent sides. Equal interior angles are one of the defining conditions for regularity.
Apothem: The perpendicular distance from a regular polygon’s center to one of its sides. It is the height of each triangular sector used to derive the polygon’s area.
Hexagonal tiling: A repeating plane pattern of congruent regular hexagons meeting edge to edge. It is the regular-hexagon tessellation used in honeycomb geometry and cellular models.
Equiangular polygon: A polygon whose interior angles all have equal measure, without requiring equal side lengths. Equal angles alone do not ensure the equal sides required for regularity.
Central angle: An angle whose vertex is the center of a circle and whose sides reach the circle. Joining the center to adjacent vertices divides a regular polygon into equal central angles.
Polygon area: The measure of the plane region enclosed by a polygon’s boundary. For a regular polygon, area equals half the product of perimeter and apothem.

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