# Compound of two pentagrams

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Compound of two pentagrams
Rank2
TypeRegular
Notation
Bowers style acronymSadag
Schläfli symbol{10/4}
Elements
Components2 pentagrams
Edges10
Vertices10
Vertex figureDyad, length (5–1)/2
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {5-{\sqrt {5}}}{10}}}\approx 0.52573}$
Inradius${\displaystyle {\sqrt {\frac {5-2{\sqrt {5}}}{20}}}\approx 0.16246}$
Area${\displaystyle {\sqrt {\frac {25-10{\sqrt {5}}}{4}}}\approx 0.81230}$
Angle36°
Central density4
Number of external pieces20
Level of complexity2
Related polytopes
ArmyDec, edge length ${\displaystyle {\sqrt {\frac {5-2{\sqrt {5}}}{5}}}}$
DualCompound of two pentagrams
ConjugateCompound of two pentagons
Convex coreDecagon
Abstract & topological properties
Flag count20
Euler characteristic0
OrientableYes
Properties
SymmetryI2(10), order 20
ConvexNo
NatureTame

The stellated decagram or sadag is a polygon compound composed of two pentagrams. As such it has 10 edges and 10 vertices.

It is the third stellation of the decagon.

Its quotient prismatic equivalent is the pentagrammic retroprism, which is three-dimensional.

## Vertex coordinates

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

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

## Variations

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