Pentadecagon

Pentadecagon
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Ped
Coxeter diagram	x15o
Schläfli symbol	{15}
Elements
Edges	15
Vertices	15
Vertex figure	Dyad, length (-1+√5+√30+6√5)/4
Measures (edge length 1)
Circumradius	$\sqrt{\frac{4+\sqrt5+\sqrt{15+6\sqrt5}}{2}} ≈ 2.40487$
Inradius	$\frac{\sqrt{7+2\sqrt5+2\sqrt{15+6\sqrt5}}}{2} ≈ 2.35232$
Area	$\frac{15\sqrt{7+2\sqrt5+2\sqrt{15+6\sqrt5}}}{4} ≈ 17.64236$
Angle	156°
Central density	1
Number of pieces	15
Level of complexity	1
Related polytopes
Army	Ped
Dual	Pentadecagon
Conjugates	Small pentadecagram, Pentadecagram, Great pentadecagram
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	I2(15), order 30
Convex	Yes
Nature	Tame

The pentadecagon is a polygon with 15 sides. A regular pentadecagon has equal sides and equal angles.

Stellations

• Small pentadecagram
• Tripentagon (compound of 3 pentagons)
• Pentadecagram
• Pentatriangle (compound of 5 triangles)
• Tripentagram (compound of 3 pentagrams)
• Great pentadecagram

External links

• Bowers, Jonathan. "Regular Polygons and Other Two Dimensional Shapes".

• Wikipedia Contributors. "Pentadecagon".