# Stellated decagon

Stellated decagon
Rank2
TypeRegular
SpaceSpherical
Notation
Schläfli symbol{10/2}
Elements
Components2 pentagons
Edges10
Vertices10
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{5+\sqrt5}{10}} ≈ 0.85065}$
Inradius${\displaystyle \sqrt{\frac{5+2\sqrt5}{20}} ≈ 0.68819}$
Area${\displaystyle \frac{\sqrt{25+10\sqrt5}}{2} ≈ 3.44095}$
Angle108°
Central density2
Number of pieces20
Level of complexity2
Related polytopes
ArmyDec
DualStellated decagon
ConjugateStellated decagram
Convex coreDecagon
Abstract properties
Euler characteristic2
Topological properties
OrientableYes
Properties
SymmetryI2(10), order 20
ConvexNo
NatureTame

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:

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