Tripentagon

Tripentagon
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Tripen
Schläfli symbol	{15/3}
Elements
Components	3 pentagons
Edges	15
Vertices	15
Vertex figure	Dyad, length (1+√5)/2
Measures (edge length 1)
Circumradius	$\sqrt{\frac{5+\sqrt5}{10}} \approx 0.85065$
Inradius	$\sqrt{\frac{5+2\sqrt5}{20}} \approx 0.68819$
Area	$\frac{3\sqrt{25+10\sqrt5}}{4} \approx 5.16143$
Angle	108°
Central density	3
Number of external pieces	30
Level of complexity	2
Related polytopes
Army	Ped, edge length $\frac{1+\sqrt5-\sqrt{30-6\sqrt5}}{4}$
Dual	Tripentagon
Conjugate	Tripentagram
Convex core	Pentadecagon
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	I2(15), order 30
Convex	No
Nature	Tame

The tripentagon or tripen is a polygon compound composed of three pentagons. As such it has 15 edges and 15 vertices.

It is the second stellation of the pentadecagon.

Its quotient prismatic equivalent is the 15-5 step prism, which is four-dimensional.

External links

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