You don't have to use gyroelongation
cross-posted from: https://lemmy.ml/post/14733630
::: spoiler 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
17 replies
I also didn't know that, that's awesome!
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!
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
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.
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
No fucking way!
That's the best piece of info I've had today!
I love to be pedantic so I'll point out that it had to be 3 equal mutually perpendicular golden ratio rectangles
and they also have to not only intersent perpendicularly, but also each of their centers must coincide.
laughs in modular origami
I just read that very slowly twice and I still don’t know either lol
If you take three 3x5 note cards, and arrange them like in the picture, you can make a d20 die for D&D
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.
It's still pretty close. 3(0.5(1+sqrt(5))) ≈ 4.854 ≈ 5, just barely over 3% higher.
Pretty neat
This is too smart and it scares me. Kill it with fire!!!
I do, friend. I do.
Must have something to do with the fact that icosahedron is dodecahedron's dual