Triacontagon
A triacontagon or 30-gon is a shape with 30 sides and 30 corners.
| Regular triacontagon | |
|---|---|
 A regular triacontagon | |
| Type | Regular polygon |
| Edges and vertices | 30 |
| Schläfli symbol | {30}, t{15} |
| Coxeter diagram |      |
| Symmetry group | Dihedral (D30), order 2×30 |
| Internal angle (degrees) | 168° |
| Dual polygon | Self |
| Properties | Convex, cyclic, equilateral, isogonal, isotoxal |
Regular triacontagon
All sides of a regular triacontagon are the same length. Each corner is 168°. All corners added together equal 5040°.
Area
The amount of space a regular triacontagon takes up is
- [math]\displaystyle{ \text{Area} = \frac{15}{4} a^2 (\sqrt{15} + 3\sqrt{3} + \sqrt{2}\sqrt{25+11\sqrt{5}}) }[/math]
a is the length of one of its sides.
Triacontagon Media
Regular triacontagon with given circumcircle. D is the midpoint of AM, DC = DF, and CF, which is the side length of the regular pentagon, is E25E1. Since 1/30 = 1/5 - 1/6, the difference between the arcs subtended by the sides of a regular pentagon and hexagon (E25E1 and E25A) is that of the regular triacontagon, AE1.
The symmetries of a regular triacontagon as shown with colors on edges and vertices. Lines of reflections are blue through vertices, and purple through edges. Gyrations are given as numbers in the center. Vertices are colored by their symmetry positions. Subgroup symmetries are connected by colored lines, index 2, 3, and 5.
en:regular polygon dissection into rhombs, boundary edges have 2 rhombus edges
regular '2n'-gon dissected into rhombs from an orthogonal projection of an 'n'-cube.
en:regular polygon dissection into rhombs
30-gon rhombic dissection2
30-gon rhombic dissectionx
en:regular polygon dissection by rhombi, random
regular star figure 2(15,1)
regular star figure 3(10,1)
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