Great heptagram

From Polytope Wiki
Jump to navigation Jump to search
Great heptagram
Regular great heptagram.svg
Rank2
TypeRegular
SpaceSpherical
Bowers style acronymGahg
Info
Coxeter diagramx7/3o
Schläfli symbol{7/3}
SymmetryI2(7), order 14
ArmyHeg
Elements
Vertex figureDyad, length 2cos(3π/7)
Edges7
Vertices7
Measures (edge length 1)
Circumradius
Inradius
Area
Angle
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[edit | edit source]

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)).

External links[edit | edit source]