Enneagram (geometry)

Enneagram
Enneagrams shown as sequential stellations
Edges and vertices 9
Symmetry group Dihedral (D9)
Internal angle (degrees) 100° {9/2}
20° {9/4}

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

The name enneagram combines the numeral prefix, ennea-, with the Greek suffix -gram. The -gram suffix derives from γραμμῆς (grammēs) meaning a line.[1]

Regular enneagram

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.[2][3] (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.[4]

Compound Regular star Regular
compound		 Regular star

Complete graph K9
{9/2}
{9/3} or 3{3}
{9/4}

Other enneagram figures


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.
The Fourth Way teachings and the Enneagram of Personality use an irregular enneagram consisting of an equilateral triangle and an irregular hexagram based on 142857.
The Bahá'í nine-pointed star

The nine-pointed star or enneagram can also symbolize the nine gifts or fruits of the Holy Spirit.[5]

See also

References

  1. ↑ γραμμή, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus
  2. ↑ Grünbaum, B. and G.C. Shephard; Tilings and Patterns, New York: W. H. Freeman & Co., (1987), ISBN 0-7167-1193-1.
  3. ↑ 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.
  4. ↑ Weisstein, Eric W. "Nonagram". From MathWorld – A Wolfram Web Resource. http://mathworld.wolfram.com/Nonagram.html
  5. ↑ Our Christian Symbols by Friedrich Rest (1954), ISBN 0-8298-0099-9, page 13.
  6. ↑ Slipknot Nonagram

Bibliography

  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26. pp. 404: Regular star-polytopes Dimension 2)
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