 Rank2
TypeRegular
SpaceSpherical
Notation
Schläfli symbol{16/2}
Elements
Components2 octagons
Edges16
Vertices16
Measures (edge length 1)
Circumradius$\sqrt{\frac{2+\sqrt2}{2}} \approx 1.30656$ Inradius$\frac{1+\sqrt2}{2} \approx 1.20711$ Area$4(1+\sqrt2) \approx 9.65685$ Angle135°
Central density2
Number of external pieces32
Level of complexity2
Related polytopes
ArmyHed, edge length $\sqrt{\frac{4+2\sqrt2-\sqrt{20+14\sqrt2}}{2}}$ ConjugateDioctagram
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryI2(16), order 32
ConvexNo
NatureTame

The stellated hexadecagon or shad is a polygon compound composed of two octagons. As such it has 16 edges and 16 vertices.

As the name suggests, it is the first stellation of the hexadecagon.

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

## Vertex coordinates

Coordinates for a stellated hexadecagon of edge length 2-2, centered at the origin, are all permutations of:

• $\left(\pm1,\,0\right),$ • $\left(\pm\frac{2+\sqrt2}{2},\,\pm\frac{2-\sqrt2}{2}\right),$ • $\left(\pm\frac{\sqrt2}{2},\,\pm\frac{\sqrt2}{2}\right).$ 