Enneagram (geometry)
Nine-pointed star polygon
From Wikipedia, the free encyclopedia
In geometry, an enneagram (🟙 U+1F7D9) is a nine-pointed plane figure. It is sometimes called a nonagram, nonangle, or enneagon.[1]
| Enneagram | |
|---|---|
Enneagrams shown as sequential stellations | |
| Edges and vertices | 9 |
| Symmetry group | Dihedral (D9) |
| Internal angle (degrees) | 100° {9/2} 20° {9/4} |
The word 'enneagram' combines the numeral prefix ennea- with the Greek suffix -gram. The gram suffix derives from γραμμῆ (grammē) meaning a line.[2]
Regular enneagram
A regular enneagram is a 9-sided star polygon. It is constructed using the same points as the regular enneagon, but the points are connected in fixed steps. Two forms of regular enneagram exist:
- One form connects every second point and is represented by the Schläfli symbol {9/2}.
- The other form connects every fourth point and is represented by the Schläfli symbol {9/4}.
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.[3][4] (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.[5]
| Compound | Regular star | Regular compound |
Regular star |
|---|---|---|---|
 Complete graph K9 |
 {9/2} |
.svg) {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 Baháʼí nine-pointed star |
.svg) A 9/3 enneagram |
 The star of Eldia from Attack on Titan |
The nine-pointed star or enneagram can also symbolize the nine gifts or fruits of the Holy Spirit.[6]
In popular culture
- The heavy metal band Slipknot previously used the {9/3} star figure enneagram[7] and currently uses the {9/4} polygon as a symbol. The prior figure can be seen on the cover of their album All Hope Is Gone.
- The symbol of Eldia from Attack on Titan is an irregular enneagram, representing the nine Titan powers.
