Enneagram

In geometry, an enneagram is a nine-pointed geometric figure. The term derives from two ancient Greek words: ennea (nine) and gramma (something written).

Enneagrams shown as sequential stellations

Regular enneagrams

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 last is sometimes also called a nonagram. 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 two 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

• The heavy metal band, Slipknot, uses the |9/3| star figure nonagram as a symbol.
• The nine-pointed star or nonagram can symbolize the nine gifts or fruits of the Holy Spirit.^[3]

See also

• Enneagon
• List of regular star polygons

References

External links

• Mathworlds page about this figure including an illustration