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 |
---|

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

The name enneagram combines the numeral prefix, * ennea- *, with the Greek suffix * -gram *. The *-gram* suffix derives from *γραμμῆς* (*grammēs*) meaning a line.^{ [2] }

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 K _{9} | {9/2} | {9/3} or 3{3} | {9/4} |

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] }

- The heavy metal band Slipknot uses the {9/3}
*star figure*enneagram as a symbol.^{ [7] }

- Nonagon (enneagon)
- List of regular star polygons

In geometry, a **polyhedron** is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. The word polyhedron comes from the Classical Greek πολύεδρον, as *poly-* + *-hedron*.

In elementary geometry, a **polytope** is a geometric object with "flat" sides. It is a generalization in any number of dimensions of the three-dimensional polyhedron. Polytopes may exist in any general number of dimensions *n* as an *n*-dimensional polytope or ** n-polytope**. Flat sides mean that the sides of a (

A **heptagram**, **septagram**, **septegram** or **septogram** is a seven-point star drawn with seven straight strokes.

A **pentagram** is the shape of a five-pointed star polygon.

In geometry, a **prism** is a polyhedron comprising an *n*-sided polygonal base, a second base which is a translated copy of the first, and *n* other faces joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases. Prisms are named for their bases; example: a prism with a pentagonal base is called a pentagonal prism. The prisms are a subclass of the prismatoids.

In geometry, a **star polygon** is a type of non-convex polygon. Only the **regular star polygons** have been studied in any depth; star polygons in general appear not to have been formally defined, however certain notable ones can arise through truncation operations on regular simple and star polygons.

In Euclidean geometry, a **regular polygon** is a polygon that is equiangular and equilateral. Regular polygons may be either **convex** or **star**. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon, if the edge length is fixed.

In geometry, a **nonagon** or **enneagon** is a nine-sided polygon or 9-gon.

In geometry, the **Schläfli symbol** is a notation of the form {*p*,*q*,*r*,...} that defines regular polytopes and tessellations.

In mathematics, a **regular polytope** is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. All its elements or *j*-faces — cells, faces and so on — are also transitive on the symmetries of the polytope, and are regular polytopes of dimension ≤ *n*.

In four-dimensional geometry, a **16-cell** is a regular convex 4-polytope. It is one of the six regular convex 4-polytopes first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century. It is also called **C _{16}**,

In geometry, a **vertex figure**, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.

In geometry, an **octagram** is an eight-angled star polygon.

A **uniform polytope** of dimension three or higher is a vertex-transitive polytope bounded by uniform facets. The uniform polytopes in two dimensions are the regular polygons.

In geometry, an **octadecagon** or 18-gon is an eighteen-sided polygon.

In geometry, a **uniform tiling** is a tessellation of the plane by regular polygon faces with the restriction of being vertex-transitive.

In geometry, a **decagram** is a 10-point star polygon. There is one regular decagram, containing the vertices of a regular decagon, but connected by every third point. Its Schläfli symbol is {10/3}.

A **dodecagram** is a star polygon or compound with 12 vertices.

In geometry, a generalized polygon can be called a **polygram**, and named specifically by its number of sides. All polygons are polygrams, but can also include disconnected sets of edges, called a compound polygon. For example, a regular pentagram, {5/2}, has 5 sides, and the regular hexagram, {6/2} or 2{3}, has 6 sides divided into two triangles.

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

This page is based on this Wikipedia article

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.