Enneagram (geometry)

In geometry, an enneagram is a nine-pointed plane figure. It is sometimes called a nonagram or nonangle.[1]

"Nonagram" redirects here. For the puzzle, see Nonogram.
Enneagram
Enneagrams shown as sequential stellations
Edges and vertices9
Symmetry groupDihedral (D9)
Internal angle (degrees)100° {9/2}
20° {9/4}
Star polygons

The name enneagram combines the numeral prefix, ennea-, with the Greek suffix -gram. The -gram suffix derives from γραμμῆς (grammēs) 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}
{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 Bahá'í nine-pointed star

The nine-pointed star or enneagram can also symbolize the nine gifts or fruits of the Holy Spirit.[6]

gollark: Well, I'd hope we replace C with something not wildly unsafe.
gollark: of course, supreme R U S T does not.
gollark: * C(++)
gollark: The C++ one stands a significantly greater chance of having security problems and memory management issues.
gollark: Ah. Hmm. It is apparently now 152KB because dependencies or something, oh well.

See also
  • Nonagon (enneagon)
  • List of regular star polygons

References
  1. http://chalkdustmagazine.com/blog/fractional-polygons/
  2. γραμμή, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus
  3. Grünbaum, B. and G.C. Shephard; Tilings and Patterns, New York: W. H. Freeman & Co., (1987), ISBN 0-7167-1193-1.
  4. 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.
  5. Weisstein, Eric W. "Nonagram". From MathWorld – A Wolfram Web Resource. http://mathworld.wolfram.com/Nonagram.html
  6. Our Christian Symbols by Friedrich Rest (1954), ISBN 0-8298-0099-9, page 13.
  7. 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)
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