Triacontadigon

A triacontadigon or icosidodecagon is a shape with 32 sides and 32 corners.

Regular triacontadigon
A regular triacontadigon
Type	Regular polygon
Edges and vertices	32
Schläfli symbol	{32}, t{16}, tt{8}, ttt{4}
Coxeter diagram
Symmetry group	Dihedral (D32), order 2×32
Internal angle (degrees)	168.75°
Dual polygon	Self
Properties	Convex, cyclic, equilateral, isogonal, isotoxal

Regular triacontadigon

All sides of a regular triacontadigon are the same length. Each corner is 168​³⁄₄°. All corners added together equal 5400°.

Area

The amount of space a regular triacontadigon takes up is

${\text{Area}}=8a^{2}\left(1+{\sqrt {2}}+{\sqrt {4+2{\sqrt {2}}}}+{\sqrt {8+4{\sqrt {2}}+2{\sqrt {20+14{\sqrt {2}}}}}}\right).$

a is the length of one of its sides.