Great hendecagram

From Polytope Wiki
Jump to navigation Jump to search
Great hendecagram
Rank2
TypeRegular
Notation
Bowers style acronymGhen
Coxeter diagramx11/4o ()
Schläfli symbol{11/4}
Elements
Edges11
Vertices11
Vertex figureDyad, length 2cos(4π/11)
Measures (edge length 1)
Circumradius
Inradius
Area
Angle
Central density4
Number of external pieces22
Level of complexity2
Related polytopes
ArmyHeng, edge length
DualGreat hendecagram
ConjugatesHendecagon, small hendecagram, hendecagram, grand hendecagram
Convex coreHendecagon
Abstract & topological properties
Flag count22
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11), order 22
ConvexNo
NatureTame

The great hendecagram is a non-convex polygon with 11 sides. It's created by taking the third stellation of a hendecagon. A regular great hendecagram has equal sides and equal angles.

It is one of four regular 11-sided star polygons, the other three being the small hendecagram, the hendecagram, and the grand hendecagram.

Vertex coordinates[edit | edit source]

Coordinates for a great hendecagram of edge length 2sin(4π/11), centered at the origin, are:

  • (1, 0),
  • (cos(2π/11), ±sin(2π/11)),
  • (cos(4π/11), ±sin(4π/11)),
  • (cos(6π/11), ±sin(6π/11)),
  • (cos(8π/11), ±sin(8π/11)),
  • (cos(10π/11), ±sin(10π/11)).

External links[edit | edit source]