Definition

1. Noun:
   • A polygon with all sides and all angles equal: A regular polygon is a two-dimensional geometric figure with straight sides where every side is the same length and every interior angle is the same measure.

Usage

• The term "regular polygon" is used in geometry to describe a specific, highly symmetric class of polygons.
• It is often contrasted with "irregular polygon," which does not have all sides and angles equal.
• Common examples include the equilateral triangle (a 3-sided regular polygon) and the square (a 4-sided regular polygon).

Examples

• Noun:
  • A stop sign is in the shape of a regular octagon.
  • The interior angle of a regular hexagon measures 120 degrees.
  • Constructing a regular pentagon with a compass and straightedge is a classic geometric problem.

Advanced Usage

• "Regular" in this context: The word "regular" specifies the condition of equal sides and angles. It is a technical term, not the common adjective meaning "usual" or "normal."
• Mathematical properties: A regular polygon is both equilateral (all sides equal) and equiangular (all angles equal). These two properties together define it.

Variants and Related Words

• Polygon (n): A general plane figure with at least three straight sides and angles.
• Regular polyhedron (n): A three-dimensional solid whose faces are all congruent regular polygons.
• Irregular polygon (n): A polygon that is not regular; its sides and/or angles are not all equal.

Synonyms

• Equilateral and equiangular polygon: This phrase is a direct description of the defining properties of a regular polygon.

Related Phrases and Concepts

• Circumscribed circle: A circle that passes through all the vertices of a regular polygon.
• Inscribed circle: A circle tangent to all the sides of a regular polygon.
• Apothem: A line from the center of a regular polygon perpendicular to one of its sides.

Noun

1. a polygon with all sides and all angles equal