In geometry, an enneagram is a nine-pointed plane figure. It is sometimes called a nonagram, nonangle, enneangle.
The word 'enneagram' combines the numeral prefix ennea- with the Greek suffix -gram. The gram suffix derives from γραμμῆ (grammē) meaning a line.γραμμή, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus.
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.Grünbaum, B. and G. C. Shephard; Tilings and patterns, New York: W. H. Freeman & Co., (1987), .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. (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.
CompoundRegular starRegularcompoundRegular starComplete 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 an equilateral triangle and an irregular hexagram based on 142857.The Baháʼí nine-pointed starA 9/3 enneagramThe 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.Our Christian Symbols by Friedrich Rest (1954), , page 13.
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.
See also List of regular star polygons Baháʼí symbols
References
Bibliography John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 26. pp. 404: Regular star-polytopes Dimension 2)
External links
Nonagram -- from Wolfram MathWorld