Rank2
TypeRegular
SpaceSpherical
Notation
Bowers style acronymHed
Coxeter diagramx16o
Schläfli symbol{16}
Elements
Edges16
Vertices16
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{2+\sqrt2+\sqrt{\frac{10+7\sqrt2}{2}}} ≈ 2.56292}$
Inradius${\displaystyle \frac{1+\sqrt{2}+\sqrt{4+2\sqrt{2}}}{2} ≈ 2.51367}$
Area${\displaystyle 4(1+\sqrt{2}+\sqrt{4+2\sqrt{2}}) ≈ 20.10936}$
Angle157.5°
Central density1
Number of pieces16
Level of complexity1
Related polytopes
ArmyHed
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryI2(16), order 26
ConvexYes
NatureTame

The hexadecagon 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 scaliform polychora.

## Vertex coordinates

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

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