Triacontagon

A triacontagon or 30-gon is a shape with 30 sides and 30 corners.

Regular triacontagon
A regular triacontagon
Type	Regular polygon
Edges and vertices	30
Schläfli symbol	{30}, t{15}
Coxeter diagram
Symmetry group	Dihedral (D30), order 2×30
Internal angle (degrees)	168°
Dual polygon	Self
Properties	Convex, cyclic, equilateral, isogonal, isotoxal

Regular triacontagon

All sides of a regular triacontagon are the same length. Each corner is 168°. All corners added together equal 5040°.

Area

The amount of space a regular triacontagon takes up is

${\displaystyle {\text{Area}}={\frac {15}{4}}a^{2}({\sqrt {15}}+3{\sqrt {3}}+{\sqrt {2}}{\sqrt {25+11{\sqrt {5}}}})}$

a is the length of one of its sides.