Pentadecagram

Pentadecagram
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Pad
Coxeter diagram	x15/4o
Schläfli symbol	{15/4}
Elements
Edges	15
Vertices	15
Vertex figure	Dyad, length (1-√5+√30+6√5)/4
Measures (edge length 1)
Circumradius	$\sqrt{\frac{4+\sqrt5-\sqrt{15+6\sqrt5}}{2}} ≈ 0.67282$
Inradius	$\frac{\sqrt{7+2\sqrt5-2\sqrt{15+6\sqrt5}}}{2} ≈ 0.45020$
Area	$\frac{15\sqrt{7+2\sqrt5-2\sqrt{15+6\sqrt5}}}{4} ≈ 3.37652$
Angle	84°
Central density	4
Number of external pieces	30
Level of complexity	2
Related polytopes
Army	Ped, edge length $\frac{1+3\sqrt5-\sqrt{30+6\sqrt5}}{4}$
Dual	Pentadecagram
Conjugates	Pentadecagon, Small pentadecagram, Great pentadecagram
Convex core	Pentadecagon
Abstract & topological properties
Flag count	30
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(15), order 30
Convex	No
Nature	Tame

The pentadecagram, or pad, is a non-convex polygon with 15 sides. It's created by taking the third stellation]] of a pentadecagon. A regular pentadecagram has equal sides and equal angles.

It is one of three regular 15-sided star polygons, the other two being the small pentadecagram and the great pentadecagram.

External links

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

• Wikipedia Contributors. "Pentadecagram".