# 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.

# Fiftystar: My 2018 Birthday Star

Every year, it is my tradition to make a star for my birthday. This is the one for today, with fifty points for my new age.

I like the view from age 50. I can see half-centuries before and after right now. To see 1968, I look into the past, which is behind me. If I look forward, I see ideas for what 2068 could be like.

# Conjoined Twin Starfish

I made this using Stella 4d: Polyhedron Navigator. You can try this program for yourself at this website.

# My 2017 Birthday Stars

I turn 49 today. This is a 49-pointed star, to mark the occasion — an old tradition of mine.

My first birthday was in 1968 — on the day I was born. A year later, on my second birthday, I turned one year old. Carry this up to the present, and that makes today, when I turn 49, my 50th birthday. For those reasons, here’s a second star, with 50 points.

# Seven Fanciful Designs for Polyhedral Throwing Stars with 7-Fold Dihedral Symmetry

I made these using Stella 4d, a program available at http://www.software3d.com/Stella.php. Any of these images may be enlarged with a click.

# Older Birthday Stars, From When I Was Younger

I started this blog in July of 2012, so the birthday stars I made in January 2012 (when I turned 44) and January 2011 (when I turned 43) did not appear here in those years. I found them, though, and will post them now.

The first two are different colorings of a 44-pointed star, from January 12, 2012, the day I turned 44:

These three are different color-versions of 43-pointed stars, from a year earlier — January 12, 2011:

I turn 48 today, so please visit the post right before this one, if you’d like to see this year’s birthday stars. =)