# Small hexadecagram

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Small hexadecagram
Rank2
TypeRegular
Notation
Bowers style acronymShed
Coxeter diagramx16/3o
Schläfli symbol{16/3}
Elements
Edges16
Vertices16
Vertex figureDyad, length 2+2-2
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {2-{\sqrt {2}}+{\sqrt {\frac {10-7{\sqrt {2}}}{2}}}}}\approx 0.89998}$
Inradius${\displaystyle {\frac {-1+{\sqrt {2}}+{\sqrt {4-2{\sqrt {2}}}}}{2}}\approx 0.74830}$
Area${\displaystyle 4(-1+{\sqrt {2}}+{\sqrt {4-2{\sqrt {2}}}})\approx 5.98642}$
Angle112.5°
Central density3
Number of external pieces32
Level of complexity2
Related polytopes
ArmyHed, edge length ${\displaystyle 1-{\sqrt {2}}+{\sqrt {2-{\sqrt {2}}}}}$
DualSmall hexadecagram
ConjugatesHexadecagon, Hexadecagram, Great hexadecagram
Convex coreHexadecagon
Abstract & topological properties
Flag count32
Euler characteristic0
OrientableYes
Properties
SymmetryI2(16), order 32
ConvexNo
NatureTame

The small hexadecagram, or shed, is a non-convex polygon with 16 sides. It's created by taking the second stellation of a hexadecagon. A regular small hexadecagram has equal sides and equal angles.

It is one of three regular 16-sided star polygons, the other two being the hexadecagram and the great hexadecagram.

It is the uniform truncation of the octagram.

## Vertex coordinates

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

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