Great enneagram

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Great enneagram
Rank2
TypeRegular
Notation
Bowers style acronymGeng
Coxeter diagramx9/4o ()
Schläfli symbol{9/4}
Elements
Edges9
Vertices9
Vertex figureDyad, length 2cos(4π/9)
Measures (edge length 1)
Circumradius
Inradius
Area
Angle20°
Central density4
Number of external pieces18
Level of complexity2
Related polytopes
ArmyEn, edge length
DualGreat enneagram
ConjugatesEnneagon, enneagram
Convex coreEnneagon
Abstract & topological properties
Flag count18
Euler characteristic0
OrientableYes
Properties
SymmetryI2(9), order 18
ConvexNo
NatureTame

The great enneagram is a non-convex polygon with 9 sides. Its created by taking the third stellation of an enneagon. A regular great enneagram has equal sides and equal angles.

It is one of two regular 9-sided star polygons, the other being the enneagram.

Vertex coordinates[edit | edit source]

Coordinates for a regular great enneagram of edge length 2sin(4π/9), centered at the origin, are:

  • (1, 0),
  • (cos(2π/9), \pmsin(2π/9)),
  • (cos(4π/9), \pmsin(4π/9)),
  • (–1/2, \pm3/2),
  • (cos(8π/9), \pmsin(8π/9)).

External links[edit | edit source]