Tripentagram

Tripentagram
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Tristar
Schläfli symbol	{15/6}
Elements
Components	3 pentagrams
Edges	15
Vertices	15
Vertex figure	Dyad, length (√5-1)/2
Measures (edge length 1)
Circumradius	$\sqrt{\frac{5-\sqrt5}{10}} \approx 0.52573$
Inradius	$\sqrt{\frac{5-2\sqrt5}{20}} \approx 0.16246$
Area	$\frac{3\sqrt{25-10\sqrt5}}{4} \approx 1.12845$
Angle	36°
Central density	6
Number of external pieces	30
Level of complexity	2
Related polytopes
Army	Ped, edge length $\frac{1-\sqrt{\frac{15-6\sqrt5}{5}}}{2}$
Dual	Tripentagram
Conjugate	Tripentagon
Convex core	Pentadecagon
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	I2(15), order 30
Convex	No
Nature	Tame

The tripentagram or tristar is a polygon compound composed of three pentagrams. As such it has 15 edges and 15 vertices.

It is the fifth stellation of the pentadecagon.

Its quotient prismatic equivalent is the pentagrammic triorthowedge, which is four-dimensional.

External links

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