Enneagram (geometry)

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This article is about the geometric polygon. For other uses, see Enneagram (disambiguation).
"Nonagram" redirects here. It is not to be confused with Nonogram.
Enneagram
Enneagon stellations.svg
Enneagrams shown as sequential stellations

In geometry, an enneagram is a nine-pointed plane figure. It is sometimes called a nonagram.

Regular enneagram[edit]

A regular enneagram (a nine-sided star polygon) is constructed using the same points as the regular enneagon but connected in fixed steps. It has two forms, represented by a Schläfli symbol as {9/2} and {9/4}, connecting every second and every fourth points respectively.

There is also a star figure, {9/3} or 3{3}, made from the regular enneagon points but connected as a compound of three equilateral triangles.[1][2] (If the triangles are alternately interlaced, this results in a Brunnian link.) This star figure is sometimes known as the star of Goliath, after {6/2} or 2{3}, the star of David.[3]

This geometrical figure should not be confused with the logic puzzles called nonograms.

8-simplex t0.svg
Complete graph K9
Nonagon.svg
Enneagon {9/1}
Star polygon 9-2.svg
Star polygon {9/2}
Star polygon 9-3.svg
Star figure {9/3} or 3{3}
Star polygon 9-4.svg
Star polygon {9/4}

Other enneagram figures[edit]

Enneagram 9-4 icosahedral.svg
The final stellation of the icosahedron has 2-isogonal enneagram faces. It is a 9/4 wound star polyhedron, but the vertices are not equally spaced.
Enneagram.png
The Enneagram of Personality and the Fourth Way teachings use an irregular enneagram consisting of a triangle and an irregular hexagram.
Bahai star.svg
The Bahá'í nine-pointed star

The nine-pointed star or enneagram can also symbolize the nine gifts or fruits of the Holy Spirit.[4]

Use in popular culture[edit]

See also[edit]

References[edit]

  1. ^ Grünbaum, B. and G.C. Shephard; Tilings and Patterns, New York: W. H. Freeman & Co., (1987), ISBN 0-7167-1193-1.
  2. ^ Grünbaum, B.; Polyhedra with Hollow Faces, Proc of NATO-ASI Conference on Polytopes ... etc. (Toronto 1993), ed T. Bisztriczky et al., Kluwer Academic (1994) pp. 43-70.
  3. ^ Weisstein, Eric W. "Nonagram". From MathWorld – A Wolfram Web Resource. http://mathworld.wolfram.com/Nonagram.html
  4. ^ Our Christian Symbols by Friedrich Rest (1954), ISBN 0-8298-0099-9, page 13.
  5. ^ Slipknot Nonagram

External links[edit]