Enneagram (geometry)
| Enneagram | |
|---|---|
 Enneagrams shown as sequential stellations |
In geometry, an enneagram is a nine-pointed geometric figure. It is sometimes called a nonagram.
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[edit] 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.[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.
 Complete graph K9 |
 Enneagon {9/1} |
 Star polygon {9/2} |
 Star figure 3{3} |
 Star polygon {9/4} |
[edit] 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 Enneagram of Personality and the Fourth Way teachings use an irregular enneagram consisting of a triangle and an irregular hexagram. |
 The Bahá'í nine-pointed star |
[edit] Use in popular culture
- Slipknot, a heavy metal band, uses the {9/3} star figure enneagram as a symbol.
- The nine-pointed star or enneagram can symbolize the nine gifts or fruits of the Holy Spirit.[4]
[edit] See also
- Nonagon (enneagon)
- List of regular star polygons
[edit] References
- ^ Grünbaum, B. and G.C. Shephard; Tilings and Patterns, New York: W. H. Freeman & Co., (1987), ISBN 0-7167-1193-1.
- ^ 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.
- ^ Weisstein, Eric W. "Nonagram". From MathWorld – A Wolfram Web Resource. http://mathworld.wolfram.com/Nonagram.html
- ^ Our Christian Symbols by Friedrich Rest (1954), ISBN 0-8298-0099-9, page 13.
[edit] External links
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