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Oh. In that case it's impossible. Tagging OP /u/Bufferadd for the notification of my answer:

Colored picture: https://i.imgur.com/oMLLKMA.jpg

Keeping the red triangle in mind, look at the orange and blue lines. The orange line must be longer than the blue line. In a perfect 5-pointed star, the blue line would be bigger.

It may be possible if you take the top of the red triangle and actually put it at the bottom, flipping the triangle upside down, and use its extensions to reach the points of the blue line.

Edit: you can play with it here: https://www.desmos.com/geometry/knmb7wgq09

While building this I realized the only way it could be perfect even if it's upside down, because of the way it's constructed.

Trying not to recompile and reupload. Try this site with this video. Let me know if that works for you.

If I start with a perfect star, I end up with this: https://www.desmos.com/geometry/y9yptodzbr

The green lines form the top spike (as I said, it ends up having to point down). The orange lines try to form the side spikes, but they are parallel and so never meet.

This is a render created with 3D software blender.

The pattern was traced over this reference photo - posted by "Islamic art gallery" user on Instagram - using 3D curves, then rendered with a flat-ish sketch style.

While your question has been answered sufficiently, I thought you might enjoy seeing the math in action. I made this interactive graph for you with Desmos.

i first figured it out with desmos, and then i tried figuring out why, and my solution is very complicated because its the only one i can think of.

also your use of "sliders" in your visualization is very nice.

Judging by how narrow the points are, as well as the spacing of the ends of each straight line being uniform rather than sinusoidal, I'm pretty sure that the shape is not an astroid, but rather of four tangent parabolas. For comparison, I've constructed both shapes in Desmos.

For an explanation on how each quadrant of the graph forms a parabola, read example 2 here.

Edit: updated Desmos plot

Woah! I didn't know something like that existed already. Btw, I used the Sketch App for Android to make this. I've made quite a few other drawings like these too.

Mekorama

I was working on hollow cubic tetrahedra, with much better graphics done on Blender, but then I had a BitLocker encryption thing happen so I'd probably need to be asked to redo all of that if it would be interesting to anyone.

To me, the GIF is trying to show both the generation of the sine and the cosine from a circle. The problem is that to do that is has to present it with a 3D view, which makes it seem more complex than it is.

https://www.desmos.com/calculator/cpb0oammx7

Click on the circle next to the "Sine Animation" and you will see the GIF you posted in two dimensions instead of three.

I found an interesting website while researching the Nonagon and also the Enneade which seems to translate texts referencing specific words

)) just google word "Merkaba", in particular this book. Ever heard about sacred geometry? I make art objects inspired by it.

)) just google word "Merkaba", in particular this book. Ever heard about sacred geometry? I make art objects inspired by it.

I am trying to find the right type of addressable LEDs that comes on a flexible wire (like xmas lights) so I can do some angles without having to cut and solder. So far I can't find ones that have the lights close enough. The solderless connectors also have versions with pigtail wires. I just need so many I want to figure out a better way. I keep failing at soldering so doing individual ones like you scares me!

That LED matrix video the animations are sweet, you need to do an updated version with color!

All those are sold by Dover who paid me a flat rate per page, no royalties.

I've printed the Ajo Coloring Book. There's not many geometrical designs in this one.

I did have an orbital mechanics coloring book which is now out of print. I'm working on a second edition. This one looks at the conic sections (circle, ellipse, parabola & hyperbola), Kepler's laws, the rocket equation & more. Lots of geometrical designs in this one.