Enneagram (geometry)

"Nonagram" redirects here. It is not to be confused with Nonogram.

Enneagram
Enneagrams shown as sequential stellations

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

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}

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

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]

See also

• Nonagon (enneagon)
• List of regular star polygons

References

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.

External links

• Mathworld's page about this figure including an illustration