 Rank2
TypeRegular
SpaceSpherical
Notation
Bowers style acronymGahd
Coxeter diagramx16/7o
Schläfli symbol{16/7}
Elements
Edges16
Vertices16
Measures (edge length 1)
Circumradius$\sqrt{2+\sqrt2-\sqrt{\frac{10+7\sqrt2}{2}}} ≈ 0.50980$ Inradius$\frac{-1-\sqrt2+\sqrt{4+2\sqrt2}}{2} ≈ 0.099456$ Area$4(-1-\sqrt2+\sqrt{4+2\sqrt2}) ≈ 0.79565$ Angle22.5°
Central density7
Number of external pieces32
Level of complexity2
Related polytopes
ArmyHed, edge length $-1-\sqrt2+\sqrt{4-2\sqrt2}$ Abstract & topological properties
Flag count32
Euler characteristic0
OrientableYes
Properties
SymmetryI2(16), order 32
ConvexNo
NatureTame

The great hexadecagram, or gahd, is a non-convex polygon with 16 sides. It's created by taking the sixth stellation of a hexadecagon. A regular great 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 hexadecagram.

It is the uniform quasitruncation of the octagon.

## Vertex coordinates

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

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