Stellated decagon

Stellated decagon
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Sadeg
Schläfli symbol	{10/2}
Elements
Components	2 pentagons
Edges	10
Vertices	10
Vertex figure	Dyad, length (1+√5)/2
Measures (edge length 1)
Circumradius	$\sqrt{\frac{5+\sqrt5}{10}} ≈ 0.85065$
Inradius	$\sqrt{\frac{5+2\sqrt5}{20}} ≈ 0.68819$
Area	$\frac{\sqrt{25+10\sqrt5}}{2} ≈ 3.44095$
Angle	108°
Central density	2
Number of pieces	20
Level of complexity	2
Related polytopes
Army	Dec
Dual	Stellated decagon
Conjugate	Stellated decagram
Convex core	Decagon
Abstract properties
Euler characteristic	2
Topological properties
Orientable	Yes
Properties
Symmetry	I2(10), order 20
Convex	No
Nature	Tame

The stellated decagon or sadeg is a polygon compound composed of two pentagons. As such it has 10 edges and 10 vertices.

As the name suggests, it is the first stellation of the decagon.

Its quotient prismatic equivalent is the pentagonal antiprism, which is three-dimensional.

Vertex coordinates

Coordinates for the vertices of a stellated decagon of edge length 1 centered at the origin are given by:

• $\left(±\frac12,\,±\sqrt{\frac{5+2\sqrt5}{20}}\right),$
• $\left(±\frac{1+\sqrt5}{4},\,±\sqrt{\frac{5-\sqrt5}{40}}\right),$
• $\left(0,\,±\sqrt{\frac{5+\sqrt5}{10}}\right).$

External links

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