Hexacontagon facts for kids
Quick facts for kids Regular hexacontagon 


A regular hexacontagon


Type  Regular polygon 
Edges and vertices  60 
Schläfli symbol  {60}, t{30}, tt{15} 
Coxeter diagram  
Symmetry group  Dihedral (D_{60}), order 2×60 
Internal angle (degrees)  174° 
Dual polygon  Self 
Properties  Convex, cyclic, equilateral, isogonal, isotoxal 
A hexacontagon or 60gon 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 twicetruncated pentadecagon, tt{15}. A truncated hexacontagon, t{60}, is a 120gon, {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 t = edge length)
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 = 2^{2} × 3 × 5, a regular hexacontagon is constructible using a compass and straightedge. As a truncated triacontagon, it can be constructed by an edgebisection of a regular triacontagon.
Dissection
Coxeter states that every zonogon (a 2mgon whose opposite sides are parallel and of equal length) can be dissected into m(m1)/2 parallelograms.
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 30cube.