# Compound of two squares

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Compound of two squares
Rank2
TypeRegular
Notation
Bowers style acronymSoc
Coxeter diagramxo4ox
Schläfli symbol{8/2}
Elements
Components2 squares
Edges8
Vertices8
Vertex figureDyad, length 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2}}\approx 0.70711}$
Inradius${\displaystyle {\frac {1}{2}}=0.5}$
Area2
Angle90°
Central density2
Number of external pieces16
Level of complexity2
Related polytopes
ArmyOc, edge length ${\displaystyle {\sqrt {\frac {2-{\sqrt {2}}}{2}}}}$
DualCompound of two squares
ConjugateCompound of two squares
Convex coreOctagon
Abstract & topological properties
Flag count16
Euler characteristic0
OrientableYes
Properties
SymmetryI2(8), order 16
Flag orbits1
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:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {\sqrt {2}}{2}},\,0\right),}$
• ${\displaystyle \left(0,\,\pm {\frac {\sqrt {2}}{2}}\right).}$

## 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.