Enneagram (geometry)

"Nonagram" redirects here. For the puzzle, see 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]

References

1. γραμμή, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus
2. Grünbaum, B. and G.C. Shephard; Tilings and Patterns, New York: W. H. Freeman & Co., (1987), ISBN 0-7167-1193-1.
3. 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.
4. Weisstein, Eric W. "Nonagram". From MathWorld – A Wolfram Web Resource. http://mathworld.wolfram.com/Nonagram.html
5. Our Christian Symbols by Friedrich Rest (1954), ISBN 0-8298-0099-9, page 13.
6. Slipknot Nonagram

Bibliography

• John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26. pp. 404: Regular star-polytopes Dimension 2)