 Rank2
TypeRegular
SpaceSpherical
Notation
Coxeter diagramx16/5o
Schläfli symbol{16/5}
Elements
Edges16
Vertices16
Measures (edge length 1)
Circumradius$\sqrt{2-\sqrt2-\sqrt{\frac{10-7\sqrt2}{2}}} ≈ 0.60134$ Inradius$\frac{1-\sqrt2+\sqrt{4-2\sqrt2}}{2} ≈ 0.33409$ Area$4(1-\sqrt2+\sqrt{4-2\sqrt2}) ≈ 2.67271$ Angle67.5°
Central density5
Number of external pieces32
Level of complexity2
Related polytopes
ArmyHed, edge length $1-\sqrt{2-\sqrt2}$ Abstract & topological properties
Flag count32
Euler characteristic0
OrientableYes
Properties
SymmetryI2(16), order 32
ConvexNo
NatureTame

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

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

It is the uniform quasitruncation of the octagram.

## Vertex coordinates

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

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