Enneagram
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2008-05-28T11:58:50Z
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{{for|the use of an Enneagram with personality issues|Enneagram of Personality}} {{for|the use of an Enneagram in relation to the teachings of [[Gurdjieff|G. I. Gurdjieff]] and his followers|Fourth Way Enneagram}}
In [[geometry]], an '''enneagram''' is a nine-pointed geometric figure. The term derives from two Greek words - '''ennea''' (nine) and '''grammos''' (something written or drawn).
[[Image:Enneagon stellations.png|thumb|150px|right|Enneagrams shown as sequential stellations]]
[[Image:Enneagram.svg|thumb|The [[Enneagram of Personality]] and [[Fourth Way Enneagram|Fourth Way Enneagram]] use an irregular enneagram, constructed from a triangle and an irregular [[hexagram]].]]
== 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}, made from the regular enneagon points but connected as a compound of three equilateral triangles.<ref>[[Branko Grünbaum|Grünbaum, B.]] and G. C. Shephard; ''Tilings and Patterns'', New York: W. H. Freeman & Co., (1987), ISBN 0-7167-1193-1.</ref> <ref>[[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.</ref> , this last is sometimes also called a [[nonagram]].
{| class=wikitable
|[[Image:Complete graph K9.svg|120px]]<BR>[[Complete graph]] K<sub>9</sub>
|[[Image:Nonagon.svg|120px]]<BR>[[Enneagon]] {9/1}
|[[Image:star polygon 9 2.png|120px]]<BR>Star polygon {9/2}
|[[Image:Star figure 9-3.png|120px]]<BR>Star figure {9/3}
|[[Image:star polygon 9 4.png|120px]]<BR>Star polygon {9/4}
|}
==See also==
* [[List of regular polytopes#Two Dimensions 2|List of regular star polygons]]
* [[Enneagon]]
[[Category:Enneagram]]
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