Enneagram (geometry)
Nine-pointed star polygon
title: "Enneagram (geometry)" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["9-(number)", "star-polygons"] description: "Nine-pointed star polygon" topic_path: "general/9-number" source: "https://en.wikipedia.org/wiki/Enneagram_(geometry)" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
::summary Nine-pointed star polygon ::
::data[format=table title="Infobox Polygon"]
| Field | Value |
|---|---|
| name | Enneagram |
| image | Enneagon stellations.svg |
| caption | Enneagrams shown as sequential stellations |
| edges | 9 |
| symmetry | Dihedral (D9) |
| angle | 100° {9/2}20° {9/4} |
| :: |
::callout[type=note] the geometric polygon ::
| name = Enneagram | image = Enneagon stellations.svg | caption = Enneagrams shown as sequential stellations | edges = 9 | schläfli = | coxeter = | symmetry = Dihedral (D9) | area = | angle = 100° {9/2}20° {9/4} | properties =}} In geometry, an enneagram (🟙 U+1F7D9) is a nine-pointed plane figure. It is sometimes called a nonagram, nonangle, or enneagon.
The word 'enneagram' combines the numeral prefix ennea- with the Greek suffix -gram. The gram suffix derives from γραμμῆ (grammē) meaning a line.
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. (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.
::data[format=table]
| Compound | Regular star | Regularcompound | Regular star |
|---|---|---|---|
| [[Image:8-simplex_t0.svg | 120px]] | ||
| Complete graph K9 | [[File:Regular star polygon 9-2.svg | 120px]] | |
| {9/2} | [[File:Regular star figure 3(3,1).svg | 120px]] | |
| {9/3} or 3{3} | [[File:Regular star polygon 9-4.svg | 120px]] | |
| {9/4} | |||
| :: |
Other enneagram figures
::data[format=table] | [[Image:Enneagram 9-4 icosahedral.svg|150px]] 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. | [[File:Enneagram.png|150px]] 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. | [[File:Bahai star.svg|150px]] The Baháʼí nine-pointed star | [[File:Nine-point star (fixed width).svg|150px]] A 9/3 enneagram | [[File:Eldia Star.svg|150px]] 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.
In popular culture
- The heavy metal band Slipknot previously used the {9/3} star figure enneagram 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.
References
Bibliography
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 26. pp. 404: Regular star-polytopes Dimension 2)
References
- (28 September 2017). "Between a square rock and a hard pentagon: Fractional polygons".
- [https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Dgrammh%2F γραμμή], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus.
- [[Branko Grünbaum. Grünbaum, B.]] and G. C. Shephard; ''[[Tilings and patterns]]'', New York: W. H. Freeman & Co., (1987), {{ISBN. 0-7167-1193-1.
- [[Branko Grünbaum. 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".
- ''Our Christian Symbols'' by Friedrich Rest (1954), {{ISBN. 0-8298-0099-9, page 13.
- "slipknot".
::callout[type=info title="Wikipedia Source"] This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page. ::