Compound of two digons

(Redirected from Tetragram)
Compound of two digons
Rank2
TypeRegular
Notation
Schläfli symbol{4/2}
Elements
Components2 digons
Edges4
Vertices4
Measures (edge length 1)
Circumradius${\displaystyle {\frac {1}{2}}=0.5}$
Area0
Angle
Central density2
Related polytopes
ArmySquare, edge length ${\displaystyle {\frac {\sqrt {2}}{2}}}$
DualCompound of two digons
ConjugateNone
Abstract & topological properties
OrientableYes
Properties
SymmetryB2, order 8
ConvexNo
NatureTame

The stellated square, also called the compound of two digons, is a regular polygon compound, being the compound of two digons. As such it has 4 edges and 4 vertices. It is degenerate if embedded in Euclidean space, as its edges coincide. However it has a non-degenerate embeddeding on the surface of a 2-sphere.

It can be formed as a degenerate stellation of the square, by extending the edges to infinity.

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

Vertex coordinates

Coordinates for the vertices of a compound of two digons of edge length 1 centered at the origin are given by:

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