# Enneagram (geometry)

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

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

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 a triangle and an irregular hexagram. 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]

## Use in popular culture

The heavy metal band Slipknot uses the {9/3} star figure enneagram as a symbol.[6]