Enneagon

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Enneagon
Regular nonagon.svg
Rank2
TypeRegular
SpaceSpherical
Bowers style acronymEn
Info
Coxeter diagramx9o
Schläfli symbol{9}
SymmetryI2(9), order 18
ArmyEn
Elements
Vertex figureDyad, length 2cos(π/9)
Edges9
Vertices9
Measures (edge length 1)
Circumradius
Inradius
Area
Angle140°
Central density1
Euler characteristic0
Number of pieces9
Level of complexity1
Related polytopes
DualEnneagon
ConjugatesEnneagram, great enneagram
Properties
ConvexYes
OrientableYes
NatureTame

The enneagon or en, sometimes referred to as a nonagon, is a polygon with 9 sides. A regular enneagon has equal sides and equal angles.

The combining prefix is e-, as in edip.

Like heptagons, enneagons are generally rare in higher polytopes.

Naming[edit | edit source]

The name enneagon is derived from the Ancient Greek ἐννέα (9) and γωνία (angle), referring to the number of vertices.

Other names include:

  • En, Bowers style acronym, short for "enneagon".

Vertex coordinates[edit | edit source]

Coordinates for an enneagon of edge length 2sin(π/9), centered at the origin, are:

  • (1, 0),
  • (cos(2π/9), ±sin(2π/9)),
  • (cos(4π/9), ±sin(4π/9)),
  • (–1/2, ±3/2),
  • (cos(8π/9), ±sin(8π/9)).

Variations[edit | edit source]

Besides the regular enneagon, other enneagons with triangular, mirror, or no symmetry exist. A few higher polytopes, such as certain swirlchora, have trigon-symmetric enneagons as facces.

Stellations[edit | edit source]

External links[edit | edit source]