Triacontadigon

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

Regular triacontadigon
Regular polygon 32.svg
A regular triacontadigon
TypeRegular polygon
Edges and vertices32
Schläfli symbol{32}, t{16}, tt{8}, ttt{4}
Coxeter diagramCDel node 1.pngCDel 3x.pngCDel 2x.pngCDel node.png
CDel node 1.pngCDel 16.pngCDel node 1.png
Symmetry groupDihedral (D32), order 2×32
Internal angle (degrees)168.75°
Dual polygonSelf
PropertiesConvex, cyclic, equilateral, isogonal, isotoxal

Regular triacontadigon

All sides of a regular triacontadigon are the same length. Each corner is 16834°. All corners added together equal 5400°.

Area

The amount of space a regular triacontadigon takes up is

[math]\displaystyle{ \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). }[/math]

a is the length of one of its sides.



Triacontadigon Media