Hexacontagon facts for kids
| Regular hexacontagon | |
|---|---|
A regular hexacontagon
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| Type | Regular polygon |
| Edges and vertices | 60 |
| Schläfli symbol | {60}, t{30}, tt{15} |
| Coxeter diagram |      |
| Symmetry group | Dihedral (D60), order 2×60 |
| Internal angle (degrees) | 174° |
| Dual polygon | Self |
| Properties | Convex, cyclic, equilateral, isogonal, isotoxal |
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 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 = 22 × 3 × 5, a regular hexacontagon is constructible using a compass and straightedge. 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.
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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- Eric W. Weisstein, Hexacontagon at MathWorld.
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Images for kids
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The symmetries of a regular hexacontagon, divided into 4 subgraphs containing index 2 subgroups. Each symmetry within a subgraph is related to the lower connected subgraphs.
