Hexacontagon

A hexacontagon or 60-gon is a shape with 60 sides and 60 corners.

 Regular hexacontagon 
A regular hexacontagon is represented by Schläfli symbol {60} and also can be constructed as a truncated triacontagon, t{30}, or a twice-truncated pentadecagon, tt{15}. A truncated hexacontagon, t{60}, is a 120-gon, {120}.

One interior angle in a regular hexacontagon is 174°, meaning that one exterior angle would be 6°.

 Area 
The area of a regular hexacontagon is (with )

and its inradius is

The circumradius of a regular hexacontagon is

This means that the trigonometric functions of π/60 can be expressed in radicals.

 Constructible
Since 60 = 22 × 3 × 5, a regular hexacontagon is constructible using a compass and straightedge.Constructible Polygon As a truncated triacontagon, it can be constructed by an edge-bisection of a regular triacontagon.

 Dissection
Coxeter states that every zonogon (a 2m-gon whose opposite sides are parallel and of equal length) can be dissected into m(m-1)/2 parallelograms.
Coxeter, Mathematical recreations and Essays, Thirteenth edition, p.141
In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. For the regular hexacontagon, m=30, and it can be divided into 435: 15 squares and 14 sets of 30 rhombs. This decomposition is based on a Petrie polygon projection of a 30-cube.
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References


 Naming Polygons and Polyhedra 


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