 Rank2
TypeRegular
SpaceSpherical
Notation
Bowers style acronymShed
Coxeter diagramx16/3o
Schläfli symbol{16/3}
Elements
Edges16
Vertices16
Measures (edge length 1)
Circumradius$\sqrt{2-\sqrt2+\sqrt{\frac{10-7\sqrt2}{2}}} ≈ 0.89998$ Inradius$\frac{-1+\sqrt2+\sqrt{4-2\sqrt2}}{2} ≈ 0.74830$ Area$4(-1+\sqrt2+\sqrt{4-2\sqrt2}) ≈ 5.98642$ Angle112.5°
Central density3
Number of external pieces32
Level of complexity2
Related polytopes
ArmyHed, edge length $1-\sqrt2+\sqrt{2-\sqrt2}$ Abstract & topological properties
Flag count32
Euler characteristic0
OrientableYes
Properties
SymmetryI2(16), order 32
ConvexNo
NatureTame

The small hexadecagram, or shed, is a non-convex polygon with 16 sides. It's created by taking the second stellation of a hexadecagon. A regular small hexadecagram has equal sides and equal angles.

It is one of three regular 16-sided star polygons, the other two being the hexadecagram and the great hexadecagram.

It is the uniform truncation of the octagram.

## Vertex coordinates

The vertices of a regular small hexadecagram of edge length 1 are given by all permutations of:

• $\left(±\frac12,\,±\frac{-1+\sqrt2+\sqrt{4-2\sqrt2}}{2}\right),$ • $\left(±\frac{1+\sqrt{2-\sqrt2}}{2},\,±\frac{-1+\sqrt2+\sqrt{2-\sqrt2}}{2}\right).$ 