Hectagon

Regular hectogon
A regular hectogon
Type	Regular polygon
Edges and vertices	100
Schläfli symbol	{100}, t{50}, tt{25}
Coxeter diagram
Symmetry group	Dihedral (D100), order 2×100
Internal angle (degrees)	176.4°
Dual polygon	Self
Properties	Convex, cyclic, equilateral, isogonal, isotoxal

In geometry, a hectogon or hecatontagon or 100-gon is a hundred-sided polygon. The sum of any hectogon's interior angles is 17640 degrees.

A regular hectogon is represented by Schläfli symbol {100} and can be constructed as a truncated pentacontagon, t{50}, or a twice-truncated icosipentagon, tt{25}.

One interior angle in a regular hectogon is 176 ²⁄₅°, meaning that one exterior angle would be 3 ³⁄₅°.

The area of a regular hectogon is (with t = edge length)

and its inradius is

The circumradius of a regular hectogon is

Because 100 = 2² × 5², the number of sides is neither a product of distinct Fermat primes nor a power of two. Thus the regular hectogon is not a constructible polygon. Indeed, it is not even constructible with the use of neusis or an angle trisector, as the number of sides is neither a product of distinct Pierpont primes, nor a product of powers of two and three.

The regular hectogon has Dih₁₀₀dihedral symmetry, order 200, represented by 100 lines of reflection. Dih₁₀₀ has 8 dihedral subgroups: (Dih₅₀, Dih₂₅), (Dih₂₀, Dih₁₀, Dih₅), (Dih₄, Dih₂, and Dih₁). It also has 9 more cyclic symmetries as subgroups: (Z₁₀₀, Z₅₀, Z₂₅), (Z₂₀, Z₁₀, Z₅), and (Z₄, Z₂, Z₁), with Z_n representing π/n radian rotational symmetry.

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