Rank2
TypeRegular
Notation
Bowers style acronymHed
Coxeter diagramx16o ()
Schläfli symbol{16}}
Elements
Edges16
Vertices16
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {2+{\sqrt {2}}+{\sqrt {\frac {10+7{\sqrt {2}}}{2}}}}}\approx 2.56292}$
Inradius${\displaystyle {\frac {1+{\sqrt {2}}+{\sqrt {4+2{\sqrt {2}}}}}{2}}\approx 2.51367}$
Area${\displaystyle 4(1+{\sqrt {2}}+{\sqrt {4+2{\sqrt {2}}}})\approx 20.10936}$
Angle157.5°
Central density1
Number of external pieces16
Level of complexity1
Related polytopes
ArmyHed
Abstract & topological properties
Flag count32
Euler characteristic0
OrientableYes
Properties
SymmetryI2(16), order 32
Flag orbits1
ConvexYes
NatureTame

The hexadecagon, or hed, is a polygon with 16 sides. A regular hexadecagon has equal sides and equal angles.

It is the uniform truncation of the octagon.

Hexadecagons and their stellations appear as faces in 8 non-prismatic scaliform polychora.

## Vertex coordinates

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

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