# Compound of two pentagons

(Redirected from Stellated decagon)
Compound of two pentagons
Rank2
TypeRegular
Notation
Schläfli symbol{10/2}
Elements
Components2 pentagons
Edges10
Vertices10
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {5+{\sqrt {5}}}{10}}}\approx 0.85065}$
Inradius${\displaystyle {\sqrt {\frac {5+2{\sqrt {5}}}{20}}}\approx 0.68819}$
Area${\displaystyle {\frac {\sqrt {25+10{\sqrt {5}}}}{2}}\approx 3.44095}$
Angle108°
Central density2
Number of external pieces20
Level of complexity2
Related polytopes
ArmyDec, edge length ${\displaystyle {\sqrt {\frac {5-{\sqrt {5}}}{10}}}}$
DualCompound of two pentagons
ConjugateCompound of two pentagrams
Convex coreDecagon
Abstract & topological properties
Flag count20
Euler characteristic2
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:

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

## Variations

The stellated decagon can be varied by changing the angle between the two component pentagons from the usual 36°. These 2-pentagon compounds generally have a dipentagon as their convex hull and remain uniform,but not regular, with pentagonal symmetry only.