Rank2
TypeRegular
Notation
Coxeter diagramx16/5o
Schläfli symbol{16/5}
Elements
Edges16
Vertices16
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {2-{\sqrt {2}}-{\sqrt {\frac {10-7{\sqrt {2}}}{2}}}}}\approx 0.60134}$
Inradius${\displaystyle {\frac {1-{\sqrt {2}}+{\sqrt {4-2{\sqrt {2}}}}}{2}}\approx 0.33409}$
Area${\displaystyle 4(1-{\sqrt {2}}+{\sqrt {4-2{\sqrt {2}}}})\approx 2.67271}$
Angle67.5°
Central density5
Number of external pieces32
Level of complexity2
Related polytopes
ArmyHed, edge length ${\displaystyle 1-{\sqrt {2-{\sqrt {2}}}}}$
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:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1-{\sqrt {2}}+{\sqrt {4-2{\sqrt {2}}}}}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {1-{\sqrt {2-{\sqrt {2}}}}}{2}},\,\pm {\frac {1-{\sqrt {2}}+{\sqrt {2-{\sqrt {2}}}}}{2}}\right).}$