# Stellated octagon

Stellated octagon Rank2
TypeRegular
SpaceSpherical
Notation
Bowers style acronymSoc
Coxeter diagramxo4ox
Schläfli symbol{8/2}
Elements
Components2 squares
Edges8
Vertices8
Measures (edge length 1)
Circumradius$\frac{\sqrt2}{2} ≈ 0.70711$ Inradius$\frac12 = 0.5$ Area2
Angle90°
Central density2
Number of external pieces16
Level of complexity2
Related polytopes
ArmyOc, edge length $\sqrt{\frac{2-\sqrt2}{2}}$ DualStellated octagon
ConjugateStellated octagon
Convex coreOctagon
Abstract & topological properties
Flag count16
Euler characteristic0
OrientableYes
Properties
SymmetryI2(8), order 16
ConvexNo
NatureTame

The stellated octagon, or soc is a polygon compound composed of two squares. As such it has 8 edges and 8 vertices.

It is the first stellation of the octagon.

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

## Vertex coordinates

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

• $\left(±\frac12,\,±\frac12\right),$ • $\left(±\frac{\sqrt2}{2},\,0\right),$ • $\left(0,\,±\frac{\sqrt2}{2}\right).$ ## Variations

The stellated octagon can be varied by changing the angle between the two component squares from the usual 45°. These 2-square compounds generally have a ditetragon as their convex hull and remain uniform, but not regular, with square symmetry only.