# Great heptagram

Great heptagram Rank2
TypeRegular
SpaceSpherical
Bowers style acronymGahg
Info
Coxeter diagramx7/3o
Schläfli symbol{7/3}
SymmetryI2(7), order 14
ArmyHeg
Elements
Edges7
Vertices7
Measures (edge length 1)
Circumradius$\frac{1}{2\sin\left(\frac{3\pi}{7}\right)} ≈ 0.51286$ Inradius$\frac{1}{2\tan\left(\frac{3\pi}{7}\right)} ≈ 0.11412$ Area$\frac{7}{4\tan\left(\frac{3\pi}{7}\right)} ≈ 0.39943$ Angle$\frac\pi7 ≈ 25.71429°$ Central density3
Euler characteristic0
Number of pieces14
Level of complexity2
Related polytopes
DualGreat heptagram
ConjugatesHeptagon, heptagram
Convex coreHeptagon
Properties
ConvexNo
OrientableYes
NatureTame

The great heptagram, great septagram, or gahg, 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), ±sin(2π/7)),
• (cos(4π/7), ±sin(4π/7)),
• (cos(6π/7), ±sin(6π/7)).