# Stellated decagram

Stellated decagram Rank2
TypeRegular
SpaceSpherical
Notation
Schläfli symbol{10/4}
Elements
Components2 pentagrams
Edges10
Vertices10
Measures (edge length 1)
Circumradius$\sqrt{\frac{5-\sqrt5}{10}} ≈ 0.52573$ Inradius$\sqrt{\frac{5-2\sqrt5}{20}} ≈ 0.16246$ Area$\sqrt{\frac{25-10\sqrt5}{4}} ≈ 0.81230$ Angle36°
Central density4
Number of pieces20
Level of complexity2
Related polytopes
ArmyDec
DualStellated decagram
ConjugateStellated decagon
Convex coreDecagon
Abstract properties
Euler characteristic0
Topological properties
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:

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