this post was submitted on 26 May 2024

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You don't have to use gyroelongation (lemmy.ml)

submitted 7 months ago by [email protected] to c/[email protected]

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cross-posted from: https://lemmy.ml/post/14733630

image description
Standard "they don't know" meme format, featuring line art of "That Feel Guy" wearing a party hat standing in a corner while other people are dancing. An image of an icosahedron formed by three mutually perpendicular golden ratio rectangles sits in front of That Feel Guy. The caption text says "They don't know that three mutually perpendicular golden ratio rectangles, with edges connecting their corners, form a regular icosahedron."

https://en.wikipedia.org/w/index.php?title=Regular_icosahedron&oldid=1219666251#Construction

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[–] [email protected] 50 points 7 months ago

I also didn't know that, that's awesome!

[–] [email protected] 28 points 7 months ago (1 children)

Is it because the golden ratio contains the square root of three which is used in constructing triangles in 3d?

Wait no, it uses the square root of 5 plus one, that is pretty magical!

[–] HonoraryMancunian 7 points 7 months ago

I assume it's because the GR has a ratio of the longer side to both sides summed. Although I can't explain it further than that lol

[–] Wootz 16 points 7 months ago* (last edited 7 months ago) (1 children)

I knew this!

On the off chance that one of you needs to model an Icosahedron / D20 in CAD, constructing three golden rectangles is often the easiest way to go, as it removes the need for calculating face angles.

[–] [email protected] 2 points 7 months ago

I knew this too! And have even used it for that same purpose when I was into designing custom rubiks twisty puzzles a few years ago

[–] [email protected] 12 points 7 months ago

No fucking way!

That's the best piece of info I've had today!

[–] [email protected] 8 points 7 months ago (1 children)

I love to be pedantic so I'll point out that it had to be 3 equal mutually perpendicular golden ratio rectangles

[–] [email protected] 6 points 7 months ago

and they also have to not only intersent perpendicularly, but also each of their centers must coincide.

[–] [email protected] 8 points 7 months ago

laughs in modular origami

[–] Juice64 4 points 7 months ago (1 children)

I just read that very slowly twice and I still don’t know either lol

[–] Dieterlan 5 points 7 months ago (1 children)

If you take three 3x5 note cards, and arrange them like in the picture, you can make a d20 die for D&D

[–] themeatbridge 6 points 7 months ago* (last edited 7 months ago) (1 children)

Almost. A 3 x 5 card does not use the golden ratio. If you cut two inches from the long side, you get a square that is 3 x 3 and a rectangle that is 2 x 3. 2/3 is not equal to 3/5.

The golden ratio occurs when a/b = (a+b)/a and it is also the ratio of the side of a pentagram to its diagonal. That's why this works.

[–] radicalautonomy 4 points 7 months ago* (last edited 7 months ago)

It's still pretty close. 3(0.5(1+sqrt(5))) ≈ 4.854 ≈ 5, just barely over 3% higher.

[–] [email protected] 4 points 7 months ago

Pretty neat

[–] [email protected] 3 points 7 months ago

This is too smart and it scares me. Kill it with fire!!!

[–] elrik 2 points 7 months ago

I do, friend. I do.

[–] [email protected] 1 points 7 months ago

Must have something to do with the fact that icosahedron is dodecahedron's dual