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:

birthday star 44 from 2012 Bbirthday star 44 from 2012

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

43 star{36_slash_17} schlafli symbol star 2012

43

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

My Birthday Stars for 2016

This year, I’m continuing my personal tradition of making stars on my birthday with numbers of points which increase each year. I’ve done this for years, and it’s based on a game I started when I turned three, and claimed the three stars of Orion’s belt as my personal property, on the grounds that they were obviously put in the sky for my benefit. Most recently, a year ago, when I turned 47, I posted a 47-pointed star on this blog.

I’m turning 48 today, so here are a couple of different colorings of 48-pointed stars containing segments through the center, {6/2} compound-triangle stars, and {8/3) star octagons, made possible by the fact that 48 = (6)(8).

star 48b

star 48a

Of course, I am turning 48 on my 49th birthday (and if that makes no sense to you, here’s the explanation), so this year I also made 49-pointed stars. They are based on 49 being the square of seven, and so contain seven each of the two types of star heptagram possible, in two different colors. For this star, also, I made two versions.

star49a

star49b

The 21st and 22nd Stellations of the Truncated Dodecahedron

Stellation of a polyhedron involves extending its faces and/or edges into space to form other polyhedra, often with a star-like appearance, which is where the words “stellation,” “stellate,” and “stellated” originate. (“Stella” is Latin for “star.”)

Since this can be done repeatedly, long stellation-series exist for many polyhedra. In the case of the truncated dodecahedron, it was the 21st and 22nd stellations which I found the most aesthetically pleasing.

Here is the 21st stellation of this polyhedron:

Trunc Dodeca 21st stellation

And here is the 22nd:

Trunc Dodeca 22nd stellation

Both of these polyhedra were created with Stella 4d, software you may try for yourself, right here.

Star and Protostar

First, Protostar:

2012 protostar ic

In nature, protostars collapse under their own gravity until enough heat is generated to ignite nuclear fusion, at which point they become stars. The image above is my interpretation of a protostar, just before the moment it becomes a star. As for Star, my post-ignition interpretation, here it is:

2012 star ic

While I did just make these images, they are simply inverted-color versions of images I made back in 2012, using Geometer’s Sketchpad. Here are the original-color versions (which I don’t like as much, myself), presented in a smaller size. You may enlarge either or both with clicks, if you wish.

2012 protostar2012 star

Star 27

sun background

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.