# Stellated dodecagon

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

Stellated dodecagon
Rank2
TypeRegular
SpaceSpherical
Notation
Bowers style acronymSedog
Schläfli symbol{12/2}
Elements
Components2 hexagons
Edges12
Vertices12
Measures (edge length 1)
Inradius${\displaystyle \frac{\sqrt3}{2} ≈ 0.86603}$
Area${\displaystyle 3\sqrt3 ≈ 5.19615}$
Angle120°
Central density2
Number of external pieces24
Level of complexity2
Related polytopes
ArmyDog, edge length ${\displaystyle \frac{\sqrt6-\sqrt2}{2}}$
DualStellated dodecagon
ConjugateStellated dodecagon
Convex coreDodecagon
Abstract & topological properties
Flag count24
Euler characteristic0
OrientableYes
Properties
SymmetryI2(12), order 24
ConvexNo
NatureTame

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:

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

## Variations

The stellated dodecagon can be varied by changing the angle between the two component hexagons from the usual 30°. These 2-hexagon compounds generally have a dihexagon as their convex hull and remain uniform, but not regular, with hexagonal symmetry only.