Rank2
TypeRegular
Notation
Bowers style acronymGahd
Coxeter diagramx16/7o
Schläfli symbol{16/7}
Elements
Edges16
Vertices16
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {2+{\sqrt {2}}-{\sqrt {\frac {10+7{\sqrt {2}}}{2}}}}}\approx 0.50980}$
Inradius${\displaystyle {\frac {-1-{\sqrt {2}}+{\sqrt {4+2{\sqrt {2}}}}}{2}}\approx 0.099456}$
Area${\displaystyle 4(-1-{\sqrt {2}}+{\sqrt {4+2{\sqrt {2}}}})\approx 0.79565}$
Angle22.5°
Central density7
Number of external pieces32
Level of complexity2
Related polytopes
ArmyHed, edge length ${\displaystyle -1-{\sqrt {2}}+{\sqrt {4-2{\sqrt {2}}}}}$
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:

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