120-gon
| Regular 120-gon | |
|---|---|
A regular 120-gon
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| Type | Regular polygon |
| Edges and vertices | 120 |
| Schläfli symbol | {120}, t{60}, tt{30}, ttt{15} |
| Coxeter diagram |
    
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| Symmetry group | Dihedral (D120), order 2×120 |
| Internal angle (degrees) | 177° |
| Dual polygon | Self |
| Properties | Convex, cyclic, equilateral, isogonal, isotoxal |
In geometry, a 120-gon is a polygon with 120 sides. The sum of any 120-gon's interior angles is 21240 degrees.
Alternative names include dodecacontagon and hecatonicosagon.
A regular 120-gon is represented by Schläfli symbol {120} and also can be constructed as a truncated hexacontagon, t{60}, or a twice-truncated triacontagon, tt{30}, or a thrice-truncated pentadecagon, ttt{15}.
One interior angle in a regular 120-gon is 177°, meaning that one exterior angle would be 3°.
The area of a regular 120-gon is (with t = edge length)
and its inradius is
The circumradius of a regular 120-gon is
This means that the trigonometric functions of π/120 can be expressed in radicals.
Since 120 = 23 × 3 × 5, a regular 120-gon is constructible using a compass and straightedge. As a truncated hexacontagon, it can be constructed by an edge-bisection of a regular hexacontagon.
The regular 120-gon has Dih120dihedral symmetry, order 240, represented by 120 lines of reflection. Dih120 has 15 dihedral subgroups: (Dih60, Dih30, Dih15), (Dih40, Dih20, Dih10, Dih5), (Dih24, Dih12, Dih6, Dih3), and (Dih8, Dih4, Dih2, Dih1). And 16 more cyclic symmetries: (Z120, Z60, Z30, Z15), (Z40, Z20, Z10, Z5), (Z24, Z12, Z6, Z3), and (Z8, Z4, Z2,Z1), with Zn representing π/n radian rotational symmetry.
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