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
Inradius
Area2
Angle90°
Central density2
Number of external pieces16
Level of complexity2
Related polytopes
ArmyOc, edge length
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[edit | edit source]

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

Variations[edit | edit source]

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.

External links[edit | edit source]