# Stellated dodecagon

Stellated dodecagon Rank2
TypeRegular
SpaceSpherical
Notation
Bowers style acronymSedog
Schläfli symbol{12/2}
Elements
Components2 hexagons
Edges12
Vertices12
Measures (edge length 1)
Inradius$\frac{\sqrt3}{2} ≈ 0.86603$ Area$3\sqrt3 ≈ 5.19615$ Angle120°
Central density2
Number of external pieces24
Level of complexity2
Related polytopes
ArmyDog
DualStellated dodecagon
ConjugateStellated dodecagon
Convex coreDodecagon
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(12), order 24
ConvexNo
NatureTame

The stellated dodecagon, or sedog, is a polygon compound composed of two hexagons. As such it has 12 edges and 12 vertices.

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

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

## Vertex coordinates

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

• $\left(±\frac12,\,±\frac{\sqrt3}{2}\right),$ • $\left(±1,\,0\right),$ • $\left(±\frac{\sqrt3}{2},\,±\frac12\right),$ • $\left(0,\,±1\right).$ 