Name This Shape

[krimmought]

Howdy Killers- 

Soccer ball is a sphere made up of hexagons and pentagons. Looks neat and I can model that reasonably well. 

What would it be if you distorted that grid in such a way as to create an egg-shaped soccer ball? So, still hexagons and pentagons, butt all stretched out into an egg shape. 

Further more how would you model this egg? If I printed all the polygons needed to make a soccer ball I could glue them up an have a sphere. There would only be two unique pieces. Shooting for a similar low unique piece count for the egg. So radial(?) symmetry is super important. 

If you were able to follow that, any advise? 🙂 

[KristianLaholm]

The soccer ball you have modeled is a polyhedron called "truncated icosahedron"

I don't think you can stretch that polyhedron without loosing the flat faces (hexagon/pentagon).

Then there is the shape called "The Egg" a "truncated hexadecahedron"

Link to some more info here: http://beadorigami.blogspot.com/2011/03/origami-interlude-egg.html 

[krimmought]

Nifty!
Thank you for that. 🙂

So, the flat planes are unwanted.
Think of the soccer ball example again.
Using the lines of those polygons and extending them to the center of the ball.
Use those to create the correct angles on the polygon sides.
I want to do that butt with the egg shape.
So, the polygons only set the edge angles. The outside and inside will each be curved to match the egg's interior and exterior radii.

Does that makes any sense? LMAO

I would like an egg shape with a given thickness divided into the minimum amount of unique shapes by a grid of distorted hexagons and pentagons.

I am going to have to add some visuals to this. Maybe.

Think symmetrical, low-poly-count egg.

[krimmought]

Seems I need what is called icosahedral symmetry.

Neat!

[Drewpan]

Hi,

AFAIK these two books are out of print and free to download.

Almost everything you want to know about Geodesics is in them. Also search for Buckminster Fuller and

you will find a wealth of information.

Cheers

Andrew

[Drewpan]

Don't know why Book two didn't attach but here it is.

[KristianLaholm]

No file provided showing how you created the soccer ball, so I don't know your workflow.

I'd create a larger truncated icosahedron and the surface loft from polyhedron face edges too center point.
Then create the egg and use the surface bodies splitting the egg into parts, this will give distorted pentagons and hexagons.

Something like this:

This is mostly repetitive work (loft and split body) and some steps could be combined, but you have to do the basic work at least one time finding the workflow.

[Warmingup1953]

Ah, Book one took me straight back to 1970 and stapling clear PVC to a mate's first dome in his parent's backyard in Sydney!... I note Book 2 didn't attach again?...so if you can reattempt I'd love to peruse it. (you may need to change the suffix>?)

[MichaelT_123]

Hwy'a Mr KrimmOught,

### Soccer ball is a sphere made up of hexagons and pentagons.  ###

Well, there are many more strategies to make one. Let's look at how Adi Does their balls (perhaps?).

In a sober state (which is not really necessary), create a couple of symmetrical axes. Asymmetry will work as well.

• Construct in circular pattern construction planes, possibly at angles around them
• Place the sphere in the middle
• Cut it by the planes
• Stitch polygonal faces
• … and you can play

Want more challenges? … as a spherical ball is only for the ones with low-kicking-ambitions.

Well then, … scale the ball ununiformly. 2D polygons are invariant to scaling in 3D space. Select different scaling factors in XYZ directions, and you will end up with an ellipsoidal-like shape,... used in countries with higher levels of kicking-self-esteem.

Not enough challenges? … want an eggeeey shape. In Fusion, you can just pull one or a couple of faces to have such. Hey, … what about the yolk inside? I think such a slight final refinement … would make a good game.

### So radial(?) symmetry is super important. ###

Well, spherical symmetries are tricky. If we are talking about flat patches approximating a sphere, there are only five congruent choices neatly proposed by Platon, and still, nobody dares to challenge him. Look at the attached videos. Some might be suited better than others, although I do think the final choice would not be as paramount as memorable post-game kicking analysis experiences at the front of a pint of Guinness, Weihenstephaner Hefe Weissbier, Pilsner, Żywiec Porter, … or put your own preference here.

Attached files:

Platonic_Golf_mono.mp4    4K_mono  (34MB)     https://a360.co/3Ke2fws

Platonic_Golf_arcd.mp4      4K_stereo  (96MB)    https://a360.co/3Oy0Tj0

Platonic_Golf_arcd.png       4K_stereo (7MB)      https://a360.co/3KeHtNr

To be viewed on 4K media devices (monitors, UHD TVs, projectors...) of reasonable performance. For the best experience, use stand-alone media applications (WMP, VLC) and the native resolution 3840x2160 - full screen. The '_arcd' files require an anaglyph red/cyan glasses, while '_al' is for active shutter glasses 3D hardware (~30 deg viewing angle is recommended). Download the files over a network, where the cost of doing so is not a concern. The files are to be used for private, non-commercial purposes only.

Eggards

MichaelT

[Drewpan]

Once more with Feeling!

I am working remotely and using Mobile Phone as the Internet so things are not quite as smooth as normal.

Book Two has the interesting Egg shapes but I thought I would include Book one for completeness.

Andrew

[Drewpan]

This is weird. I attached the first one exactly the same way.

Changed the name this time. Is only 39MB so is not too big.

[Drewpan]

Ok Guys,

That's three failures to attach a file and it came from the same place as the first one that attached successfully.

Any ideas why this is not working?

How else can I attach a file? Drag and Drop doesn't seem to work here.

Andrew

[krimmought]

Oh, that looks so good!
Thank you very much. 🙂

[Drewpan]

One last try

[TheCADWhisperer]

@Drewpan 

I would be hesitant about posting copyrighted material - even if it is out of print.

[krimmought]

Golly.

There is a lot going on in your reply. 🙂

Thank you for all that information!

All of you folks are so very kind.

[Drewpan]

Hi,

Under normal circumstances I would not do this at all.

My research indicated that it was not only out of print but also freely available for personal use.

I considered that this would be personal use as it is a very narrow topic and a specific instance.

I will take on board your comment.

Thanks

Andrew

[krimmought]

Yes... 

You certainly wouldn't want to upset the publishers.

They monitor this forum, you know?

Oh, yes.

Litigious little bastards.

Next thing you know you're up their in the gulag.

Frozen.

Oh, how I do hate publishers!

[krimmought]

Alright.

Think I have it worked out.

Will post some images once I finish.

Modeled the pentagon and hexagon.

Assembled them into half a sphere's worth.

Measured that to proportionately space the elliptical end.

Angled some planes.

Parted the hell outta some bodies.

Looking real good.

Thanks again for all your help, folks!

[krimmought]

something like thisNever you mind that back/left half.

The ball end is easy.

I left out a few bits that you might better see the angles.

Is all stretchy.

I love it.

Now to route this big pig into pink foam existence...

You folks are the best!

Thanks again. 🙂