# Great heptagram

Great heptagram
Rank2
TypeRegular
Notation
Bowers style acronymGahg
Coxeter diagramx7/3o ()
Schläfli symbol{7/3}
Elements
Edges7
Vertices7
Measures (edge length 1)
Circumradius${\displaystyle {\frac {1}{2\sin \left({\frac {3\pi }{7}}\right)}}\approx 0.51286}$
Inradius${\displaystyle {\frac {1}{2\tan \left({\frac {3\pi }{7}}\right)}}\approx 0.11412}$
Area${\displaystyle {\frac {7}{4\tan \left({\frac {3\pi }{7}}\right)}}\approx 0.39943}$
Angle${\displaystyle {\frac {\pi }{7}}\approx 25.71429^{\circ }}$
Central density3
Number of external pieces14
Level of complexity2
Related polytopes
ArmyHeg, edge length ${\displaystyle 2\cos {\frac {3\pi }{7}}}$
DualGreat heptagram
ConjugatesHeptagon, heptagram
Convex coreHeptagon
Abstract & topological properties
Flag count14
Euler characteristic0
OrientableYes
Properties
SymmetryI2(7), order 14
ConvexNo
NatureTame

The great heptagram is a polygon with 7 sides. Its created by taking the second stellation of a heptagram. A regular great heptagram has equal sides and equal angles.

It is one of two regular 7-sided star polygons, the other being the heptagram.

## Vertex coordinates

Coordinates for a regular heptagram of edge length 2sin(3π/7), centered at the origin, are:

• (1, 0),
• (cos(2π/7), \pmsin(2π/7)),
• (cos(4π/7), \pmsin(4π/7)),
• (cos(6π/7), \pmsin(6π/7)).