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The 18 pages that link to Regular polygon, each with the reason it gives.

• CircleCompared with: As the number of sides grows, regular polygons can approximate a circle.

• Equilateral triangleNarrower topic: It is the three-sided member of the regular polygons.

• PolygonBroader topic: Regular polygons provide highly symmetric shapes for tilings and constructions.

• Interior angleBroader topic: Its equal angles each measure the interior-angle sum divided by the number of vertices.

• TessellationBroader topic: Regular polygons provide the simplest test of which single shapes tile the plane.

• PerimeterBroader topic: Its perimeter is the number of sides multiplied by one side length.

• Geometric constructionBroader topic: Constructibility of regular polygons is a central test case for the classical rules.

• Rotational symmetryBroader topic: A regular n-sided polygon is preserved by rotations in steps of 360°/n.

• Convex polygonCompared with: Regularity concerns equal sides and angles, whereas convexity concerns containment of segments.

• Platonic solidNarrower topic: Every face of a Platonic solid is a regular polygon.

• Schläfli symbolBroader topic: The one-entry symbol {p} identifies a regular polygon with p sides.

• Reuleaux triangleNarrower topic: The Reuleaux triangle’s construction begins with a regular polygon but replaces its sides with arcs.

• Fermat polygonal number theoremRelated: The geometric shapes give polygonal numbers their names and dot-arrangement interpretation.

• Star polygonNarrower topic: Star polygons connect selected vertices of a regular polygon.

• DecagonRelated: A regular decagon is the best-known symmetric form of the shape.

• Gilbert–Pollak conjectureRelated: Symmetric point configurations provide test cases for comparing Steiner and spanning trees.

• Honeycomb theoremRelated: Among polygons with a fixed number of sides and area, regular shapes provide the relevant perimeter bounds.

• Internal and external anglesBroader topic: Its symmetry makes every interior angle and every exterior turn equal.