# Tag Archives: enneagram

## Three Regular Enneagrams, Each Made of Three Equilateral Triangles

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# The Regular Enneagon, and Three Regular Enneagrams

The red figure above is a regular enneagon, or nine-sided polygon, and it has three regular enneagrams (or “star enneagons”) inside it. The light blue figure is called a {9,2} enneagram. The green figure can be viewed two ways: as a {9,3} enneagram, or as a compound of three equilateral triangles. Finally, the yellow figure is a {9,4} enneagram.

To see what these numbers in braces mean, just take a look at one of the yellow enneagram’s vertices, then follow one of the yellow segments to the next vertex it touches. Count the vertices which are skipped, and you’ll notice each yellow segment connects every fourth vertex, giving us the “4” in {9,4}. The “9” in {9,4} comes from the total number of vertices in this enneagram, as well as the total number of segments it has. The blue and green enneagrams are analogous to the yellow one. These pairs of numbers in braces are known as Schläfli symbols.

I should mention that some people call these figures “nonagons” and “nonagrams.” Both “ennea- and “nona-” refer to the number nine, but the latter prefix is derived from Latin, while the former is based on Greek. I prefer to use the Greek, since that is consistent with such Greek-derived words as “pentagon” and “hexagon.”

Finally, there is also an “enneagram of personality,” in popular culture, which some use for analyzing people. Aside from this mention of it, that figure is not addressed here — nor is the nine-pointed star used as a symbol for the Bahá’í faith. However, it’s easy to find information on those things with Google-searches, for those who are interested.

# Nine (2015) / Nine (2013)

# Star 27

Do not attempt to construct this with compass and straight edge . . . unless you just have extra time you want to waste. If constructing this were possible, then also possible would be the construction of a regular enneagon, and that has been proven impossible. To make this, I had to “cheat” by using rotations of 40°, using *Geometer’s Sketchpad*, which will let you play the construction-game by Euclid’s rules, or not, as you choose.

## Pulsating Cuboctahedron, Featuring Enneagrammic Mandalas

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The enneagramic mandalas on the square faces of this cuboctahedron are from the last post, with inverted-color, smaller versions of the same image on the triangular faces. These mandalas were created using *Geometer’s Sketchpad* and *MS-Paint*. Projecting them onto the faces of the cuboctahedron, and then creating this rotating, pulsating .gif image, however, took a third program: *Stella 4d*, which you can buy, or try for free, at http://www.software3d.com/Stella.php.

## Ten Enneagrams

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These enneagrams are of the {9/3} variety, which means each one is made of three concentric, equilateral triangles. One of these enneagrams is at the center; the other nine surround it.