# Far from exciting, but I had a breakthrough

I use SU all the time for kitchen and bath design as well as architectural massing and renderings. Sometimes I just sit and doodle.
A while back, I wanted to create a soccer ball with basic SU tools and zero math. Seemed easy enough, I could do it with other modeling programs.
Normally, I would place my polygons flat and then create rotation paths with a circle. I would rotate to the intersection of the circle and repeat. Since SketchUp doesn’t use circles, I couldn’t quite make it work.
Finally, it dawned on me that I only needed the start, end and center. By using the basic Arc or Pie tools, I was finally able to create proper rotation path and thus perfect geometric spheres.

Very embarrassed that it took me so long to figure out.

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If you need regular polyhedra in future, you could use my plug-in Polyhedra from the SketchUcation plug-in store:

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Did you see @TheOnlyAaron’s video on YouTube at all? That was a while ago, and I don’t remember now how he did it, but could always watch it again.

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I’ll keep that in mind. Thank you.

Now that I’ve solved the puzzle on my own, I went back and watched his icosahedron and dodecahedron builds. The arc tool was the key for his as well, but he did have one little geometry nugget that saves a few steps.

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I’m always afraid to use the arc tool in SU to solve geometry problems because the segmentation can yield inaccurate results. BTW, I posted my own version of platonic solid in a thread here. Now I have to see if I can do it again.

The Arc works in this case because you aren’t relying on the smoothness. You could make it a two segment arc, but if you have the center, start and end, it is exact as anything else.

I see that even your “toy” was built using the 3 golden rectangles. A great starting point for normals.
My puzzle was just being able to rotate any two connected planes to where they shared an edge. This has now taken me down a rabbit hole, and I’m not getting my work done.

Years ago, @jean_lemire_1 posted a beautiful tutorial about constructing a dodecahedron without using arcs or circles. He started with a cube.

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I’ll have to look that one up. Sounds intriguing.

It was some forum generations ago so probably not in the current one. I pinged Jean in the hope he would find and re-post it.

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Yes. Click in sequence on the scenes tabs of this SU file for ideas.

Platonic solids.skp (227.8 KB)

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Some of what you have is what Ann Tyng’s exercise had in it, but the relationship of icosahedron faces to dodecahedron verticies was a neat insight.

A soccer ball or football as we call it here is made of pentagons and hexagons. Yours has only pentagons…

Once I figure out how to rotate and align, the rest was easy!

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Well actually, not always.

I mean sure, the standard black and while ball we all have in mind yeah.
But turns out that most “official” balls for world / euro cups and such are not. There was even one that was technically a… 6 faces volume. So, a cube. and another (same video) is actually a dodecahedron.

Matt parker did some videos on it, he is quite passionate about that issue (properly representing footballs)

Turns out that “big football” has been lying to us for years !

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I like that Prem league ball. I guess a base ball is technically a plane since it only has two surfaces

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Click in sequence on the scenes tabs of this SU file for ideas.

Truncated icosahedron.skp (180.6 KB)

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So the last step would be to use the Soap Bubble plugin to inflate the thing, yes?

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maybe. I don’t really use plugins.
It was never really about a soccer/foot ball/truncated icosahedron, just the rotating of things properly. The more things I can do by brute force, the better I feel.

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