Pentadecagon

Pentadecagon
(OFF file)
Rank	2
Type	Regular
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	${\sqrt {\frac {4+{\sqrt {5}}+{\sqrt {15+6{\sqrt {5}}}}}{2}}}\approx 2.40487$
Inradius	${\frac {\sqrt {7+2{\sqrt {5}}+2{\sqrt {15+6{\sqrt {5}}}}}}{2}}\approx 2.35232$
Area	${\frac {15{\sqrt {7+2{\sqrt {5}}+2{\sqrt {15+6{\sqrt {5}}}}}}}{4}}\approx 17.64236$
Angle	156°
Central density	1
Number of external pieces	15
Level of complexity	1
Related polytopes
Army	Ped
Dual	Pentadecagon
Conjugates	Small pentadecagram, Pentadecagram, Great pentadecagram
Abstract & topological properties
Flag count	30
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(15), order 30
Flag orbits	1
Convex	Yes
Nature	Tame

The pentadecagon, or ped, 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".