Pentatriangle

Pentatriangle
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Pentri
Schläfli symbol	{15/5}
Elements
Components	5 triangles
Edges	15
Vertices	15
Vertex figure	Dyad, length 1
Measures (edge length 1)
Circumradius	$\frac{\sqrt3}{3} \approx 0.57735$
Inradius	$\frac{\sqrt3}{6} \approx 0.28868$
Area	$\frac{5\sqrt3}{4} \approx 2.16506$
Angle	60°
Central density	5
Number of external pieces	30
Level of complexity	2
Related polytopes
Army	Ped, edge length $\frac{1-\sqrt5+\sqrt{\frac{10+2\sqrt5}{3}}}{4}$
Dual	Pentatriangle
Conjugate	Pentatriangle
Convex core	Dodecagon
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(15), order 30
Convex	No
Nature	Tame

The pentatriangle, or pentri, is a polygon compound composed of 5 triangles. As such it has 15 edges and 15 vertices. It is the fourth stellation of the pentadecagon.

Its quotient prismatic equivalent is the triangular pentachoroorthowedge, which is five-dimensional.

External links

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