Enneagram (geometry)

Nine-pointed star polygon

This article is about the geometric polygon. For other uses, see Enneagram (disambiguation).

"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}
Star polygons

* * *

* pentagram
* hexagram
* heptagram
* octagram
* enneagram
* decagram
* hendecagram
* dodecagram

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In geometry, an enneagram (🟙 U+1F7D9) is a nine-pointed plane figure. It is sometimes called a nonagram, nonangle, or enneagon.[1]

The word 'enneagram' combines the numeral prefix ennea- with the Greek suffix -gram. The gram suffix derives from γραμμῆ (grammē) meaning a line.[2]

## Regular enneagram[edit]

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

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Complete graph K9 |
{9/2}  |
{9/3} or 3{3}  |
{9/4}

## Other enneagram figures[edit]

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 |
A 9/3 enneagram

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

## In popular culture[edit]

* The heavy metal band Slipknot previously used the {9/3} star figure enneagram[7] and currently uses the {9/4} polygon as a symbol. The prior figure can be seen on the cover of All Hope Is Gone.

## See also[edit]

* List of regular star polygons
* Baháʼí symbols

## References[edit]

1. ^ "Between a square rock and a hard pentagon: Fractional polygons". 28 September 2017.
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". mathworld.wolfram.com.
6. ^ Our Christian Symbols by Friedrich Rest (1954), ISBN 0-8298-0099-9, page 13.
7. ^ "slipknot". eBay.

Bibliography

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

## External links[edit]

* Media related to Enneagram at Wikimedia Commons
* Nonagram -- from Wolfram MathWorld

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Polygons (List)

Triangles|

* Acute
* Equilateral
* Ideal
* Isosceles
* Kepler
* Obtuse
* Right

Quadrilaterals|

* Antiparallelogram
* Bicentric
* Crossed
* Cyclic
* Equidiagonal
* Ex-tangential
* Harmonic
* Isosceles trapezoid
* Kite
* Orthodiagonal
* Parallelogram
* Rectangle
* Right kite
* Right trapezoid
* Rhombus
* Square
* Tangential
* Tangential trapezoid
* Trapezoid

By number
of sides|

| 1–10 sides|

* Monogon (1)
* Digon (2)
* Triangle (3)
* Quadrilateral (4)
* Pentagon (5)
* Hexagon (6)
* Heptagon (7)
* Octagon (8)
* Nonagon/Enneagon (9)
* Decagon (10)

|

11–20 sides|

* Hendecagon (11)
* Dodecagon (12)
* Tridecagon (13)
* Tetradecagon (14)
* Pentadecagon (15)
* Hexadecagon (16)
* Heptadecagon (17)
* Octadecagon (18)
* Icosagon (20)

>20 sides|

* Icositrigon (23)
* Icositetragon (24)
* Triacontagon (30)
* 257-gon
* Chiliagon (1000)
* Myriagon (10,000)
* 65537-gon
* Megagon (1,000,000)
* Apeirogon (∞)

Star polygons

* Pentagram
* Hexagram
* Heptagram
* Octagram
* Enneagram
* Decagram
* Hendecagram
* Dodecagram

Classes|

* Concave
* Convex
* Cyclic
* Equiangular
* Equilateral
* Infinite skew
* Isogonal
* Isotoxal
* Magic
* Pseudotriangle
* Rectilinear
* Regular
* Reinhardt
* Simple
* Skew
* Star-shaped
* Tangential
* Weakly simple

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