Small pentadecagram

Small pentadecagram
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Sped
Coxeter diagram	x15/2o
Schläfli symbol	{15/2}
Elements
Edges	15
Vertices	15
Vertex figure	Dyad, length (1+√5+√30-6√5)/4
Measures (edge length 1)
Circumradius	$\sqrt{\frac{4-\sqrt5+\sqrt{15-6\sqrt5}}{2}} ≈ 1.22930$
Inradius	$\frac{\sqrt{7-2\sqrt5+2\sqrt{15-6\sqrt5}}}{2} ≈ 1.12302$
Area	$\frac{15\sqrt{7-2\sqrt5+2\sqrt{15-6\sqrt5}}}{4} ≈ 8.42264$
Angle	132°
Central density	2
Number of external pieces	30
Level of complexity	2
Related polytopes
Army	Ped, edge length $\frac{2-\sqrt5+\sqrt{15-6\sqrt5}}{2}$
Dual	Small pentadecagram
Conjugates	Pentadecagon, 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 small pentadecagram, or sped, is a non-convex polygon with 15 sides. It's created by taking the first stellation of a pentadecagon. A regular small pentadecagram has equal sides and equal angles.

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

External links

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

• Wikipedia Contributors. "Pentadecagram".