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## Mathematicians Solve the Topological Mystery Behind the "Brazuca" Soccer Ball144

KentuckyFC (1144503) writes "In the 1970 World Cup in Mexico, teams used a new kind of ball called the Telstar made from 12 black pentagonal panels and 20 white hexagonal panels. This ball has icosahedral symmetry and its own molecular analogue in the form of C60, the famous soccer ball-shaped fullerene. In 2006, a new ball called the TeamGeist was introduced at the World Cup in Germany. This was made of 14 curved panels that together gave it tetrahedral symmetry. This also had a molecular analogue with tetrahedral symmetry among the fullerenes. Now teams at the current World Cup in Brazil are playing with yet another design: the Brazuca, a ball constructed from six panels each with a four-leaf clover shape that knit together like a jigsaw to form a sphere. This has octahedral symmetry. But here's question that has been puzzling chemists, topologists and..errr...soccer fans: is there a molecular analogue of the Brazuca? Or put another way, can fullerenes have octahedral symmetry? Now a pair of mathematicians have finally solved this problem. They've shown that fullerenes can indeed have octahedral symmetry just like the Brazuca, although in addition to hexagonal and pentagonal carbon rings, the ball-shaped molecules must also have rings of 4 and 8 carbon atoms. The next stage is to actually synthesis one of these fullerenes, perhaps something to keep chemists occupied until the 2018 World Cup in Russia."
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## Mathematicians Solve the Topological Mystery Behind the "Brazuca" Soccer Ball

• #### And another question (Score:5, Insightful)

on Thursday July 10, 2014 @08:28AM (#47423635) Homepage

Which ball is the best for the players?

Personally I prefer the Telstar.

• #### Re: (Score:1)

by Anonymous Coward

Which ball is the best for the players?

Personally I prefer the Telstar.

The one in the back of the net.

• #### Re: (Score:2, Insightful)

*sigh*

Is this soccer thing still going on? Once the US was out of it, I lost interest and figured this would have been done and over with by now.

Its like what, 4 years or something before soccer starts up again when this one is done?

:)

• #### Re: (Score:1)

by Anonymous Coward

Well, the REST OF THE WORLD is interested and doesnt give a shit about american football.

• #### Re: (Score:1)

by Anonymous Coward

the black and white ball is also what i picture as being a 'soccer ball'.. its what we had as kids, what schools had years later...

the other newer designs are just gimmicks to sell 'official' merchandise. dont see much real improvement in the physics of the ball itself. at least we aren't watching a bunch of sweaty guys running around for 90 minutes in some space-aged skin tight spandex-y body suit.

• #### Re: (Score:2)

Yeah, wow, I didn't realize that form was so relatively recent. I had thought that's what soccer balls were "always" like. (From the Wikipedia page, they actually came out before 1970..)

• #### Re: (Score:2)

Yeah, wow, I didn't realize that form was so relatively recent. I had thought that's what soccer balls were "always" like. (From the Wikipedia page, they actually came out before 1970..)

They probably started as nothing more than an inflated animal bladder, but I do recall seeing one of these http://comeheretome.files.word... [wordpress.com]

• #### Re: (Score:2)

dont see much real improvement in the physics of the ball itself.

That's not what the players think. Many of them come out and bitch and moan about the changes in soccer ball design because it feels and plays different. Many teams complained that the Germans had an unfair advantage in 2006 because they got to play with the new ball before everyone else and thus had more training using it. Physicists have chimed in on it too saying the 2006 ball is likely to mostly affect keeping as the smoother surface with less seams makes the balls trajectory unstable if spinning in fli

• #### Re: (Score:2)

The Telstar is the only one that says "soccer" to me.

• #### Re: (Score:1)

by Anonymous Coward

The Telstar is the only one that says "soccer" to me.

That's likely because you're looking at a knockoff. A real Telstar, made by Adidas AG, would say "football", not "soccer" ^^

• #### Re: (Score:2)

I do wonder what Bobby Charlton could have done with a modern ball considering he did this [youtube.com] with a ball made of inch-thick cowhide with a concrete core that absorbed half its weight in water on a typical English match day.

• #### Re: (Score:2)

I do wonder what Bobby Charlton could have done with a modern ball considering he did this [youtube.com] with a ball made of inch-thick cowhide with a concrete core that absorbed half its weight in water on a typical English match day.

Jesus fuck. That's your go-to amazing moment for soccer? Don't waste your time watching the video, kids. The dude kicks the ball from a moderate distance at moderate speed and it goes into the net.

• #### Re: (Score:2)

Jesus fuck. That's your go-to amazing moment for soccer? Don't waste your time watching the video, kids. The dude kicks the ball from a moderate distance at moderate speed and it goes into the net.

On behalf of those of us who didn't do so well in gym class ... that would be somewhat amazing. Even if the net was empty. ;-)

• #### why new balls (Score:5, Interesting)

on Thursday July 10, 2014 @08:37AM (#47423695)

http://en.wikipedia.org/wiki/F... [wikipedia.org]

It looks like every world cup but perhaps a couple has had a different stitch pattern on the ball. Is there really that much need for innovation? I think it might be cool to have a "better ball" but doesn't the sport at some point lose something from the equipment changing so frequently? Comparing stats when the balls have different characteristics like how smoothly they'll roll, air resistance etc must be the explanation for soccer riots.

• #### Re:why new balls (Score:5, Insightful)

by Anonymous Coward on Thursday July 10, 2014 @08:56AM (#47423817)

Comparing stats when the balls have different characteristics like how smoothly they'll roll, air resistance etc must be the explanation for soccer riots.

No, the lack of any sort of concept of what's really important and what isn't causes ALL sports related riots.

Seems most of the point of team sports is for the mediocre to identify with something bigger and more glorious than their own lives and then to cling to that constructed image fiercely, as though the effort they expend in doing so is proof of its reality. Hence they say "WE won" when they themselves were not out on that field because it has become an extension of their ego. Fighting and rioting over it also provides the assumption that something important must be going on. Something worth fighting and rioting over. It's false of course. It appeals to people who have no concept of the profound, the sacred, or the meaningful.

• #### Re: (Score:2)

Very well said, Sir or Madame AC!

• #### Re: (Score:1)

by Anonymous Coward

A few hundred years ago, that was the point of religion. Some people still aren't over that, so I imagine sports are here to stay.

• #### Re: (Score:2)

A few hundred years ago, that was the point of religion. Some people still aren't over that, so I imagine sports are here to stay.

Religion is the exact opposite. Religion necessitates the humility of the follower in the face of the divine. You don't go to a Christian church and shout "FUCK YEAH, JESUS! WHOOOO!" for 2 hours.

Religious institutions can become corrupt and seek power and wealth from their followers. When an institution becomes corrupt to the extent that followers are controlled and the leaders claim to be divine or close to divine, we call it a cult.
Religious followers can become blind zealots who seek the spread of th

• #### Re: (Score:2)

You don't go to a Christian church and shout "FUCK YEAH, JESUS! WHOOOO!" for 2 hours.

Never seen an evangelical mega-church? You don't pass 10k members by without a lot of up-with-people let's-celebrate. But then again, they barely mention Jesus, and certainly don't mention sin - wouldn't want to offend anyone in the audience after all. But then, that's exactly why the fundies hate the evangelicals.

There are a couple of big religions that grew during medieval times, and so are very feudal in their structure, with God as the king-of-kings, and humility and suborning one's will to him are t

• #### Re: (Score:2)

Two from Mitchell & Webb:

• #### Re:why new balls (Score:5, Insightful)

on Thursday July 10, 2014 @11:45AM (#47425023)
>Hence they say "WE won" when they themselves were not out on that field

I agree with most of your post, but when I made that claim to a friend who's into sports, he pointed out that the fans are financing the whole thing.
• #### Re: (Score:2)

But this team lives close to me therefore it is the most important thing in my life to see them win.

• #### Re: (Score:1)

Apparently sports riots in soccer come about because the soccer teams are related to various political factions, at least throughout most of Europe.
• #### Re: (Score:3)

It looks like every world cup but perhaps a couple has had a different stitch pattern on the ball. Is there really that much need for innovation?

In a word: No. Even to discerning players, there's no practical gameplay difference between this ball and the typical hexagons-and-pentagons design. There is no need for innovation in order to improve the sport - the outcome of the World Cup matches probably would have been the same with a \$30 ball. There is that kind of need, however, for Adidas to sell a who

• #### Re:why new balls (Score:4, Funny)

on Thursday July 10, 2014 @09:07AM (#47423891) Homepage

There is that kind of need, however, for Adidas to sell a whole shitload of super-cool-awesome-double-plusgood soccer balls every couple of years at inflated prices.

I see what you did there. ;-)

• #### Re:why new balls (Score:4, Interesting)

on Thursday July 10, 2014 @09:10AM (#47423911)
But if there is no difference between ball designs then why do we never see shots like these [youtube.com] anymore?
• #### Re:why new balls (Score:4, Informative)

<`moc.stibkeeg' `ta' `ylamona'> on Thursday July 10, 2014 @09:58AM (#47424259) Homepage

Good question, but I'd argue it's more about shot selection than anything. Most of those goals were well beyond the 18 (the penalty box). If you're comparing to recent games (yeah, I'm in the US, I still call them games, shoot me), like in the World Cup, you see very few shots outside the 18. An extreme example would be the Netherlands-Argentina game where they both played very defensive games. Even in games like Germany-Brazil, it seemed Germany was more about finesse and getting the ball deep inside the box to increase chances of the shot going in the back of the net. Even on free kicks near the 18, not many are even an attempt on goal, but rather crosses.

I used to play, and IMHO shot shaping is more about technique (and shot selection) than the design of the ball. You'll notice in your video a lot of them were hit with the outside of the foot, right or left, and that's the easiest way to get it to curve to the outside. You don't see many players these days even attempting those.

• #### Re: (Score:2)

I may have not completed my thought and main point, although it may be obvious enough... the shots in the video being further out will end up having much more curve on them by the time they reach the goal. The same shot closer to the goal won't have as much noticeable curve, of course.
• #### Re: (Score:2)

Because you're not paying attention?

The Argentinians missed what looked like a great goal in the making yesterday except that it curved away from the goal.

Also the 2006 ball had physicists warning that the ball will behave more like a baseball and that it'll make quite nice curves while spinning, and act chaotically when not.

• #### Re: (Score:2)

But if there is no difference between ball designs then why do we never see shots like these [youtube.com] anymore?

Not enough sidewind? Seriously the biggest of the curves can not be produced by spinning balls, it is the wind carrying it.

• #### Re: (Score:1)

by Anonymous Coward

Actually there was a lot of complaints about the one used in South Africa in 2010 because it was said to be "very unpredictable especially over a great distance", by many players. So maybe it doesn't apply to the Brazuca, and maybe the complaints are just anecdotal, but I wouldn't be so categorical about:

There is no need for innovation in order to improve the sport - the outcome of the World Cup matches probably would have been the same with a \$30 ball

• #### Re: (Score:3)

Actually there was a lot of complaints about the one used in South Africa in 2010 because it was said to be "very unpredictable especially over a great distance", by many players. So maybe it doesn't apply to the Brazuca, and maybe the complaints are just anecdotal, but I wouldn't be so categorical about

Which only serves to further my point: by "innovating" when there was no particular need, Adidas created a f^%\$ed up ball in 2010, which they then needed further innovation to fix. Pointless - but they so

• #### Re: (Score:1)

by Anonymous Coward

http://en.wikipedia.org/wiki/F... [wikipedia.org]

It looks like every world cup but perhaps a couple has had a different stitch pattern on the ball. Is there really that much need for innovation? I think it might be cool to have a "better ball" but doesn't the sport at some point lose something from the equipment changing so frequently? Comparing stats when the balls have different characteristics like how smoothly they'll roll, air resistance etc must be the explanation for soccer riots.

I agree. After a certain point, innovation becomes rather pointless, but that wouldn't feed the massive revenue streams that rely on selling "new and improved" every 6-12 months.

The same could be said for running or basketball shoes. The biggest "innovation" those products have had in the last 5 years is puking neon colors all over them in an attempt to find fashion and style.

• #### Re: (Score:2)

It looks like every world cup but perhaps a couple has had a different stitch pattern on the ball.

No, it doesn't. They were all somewhat different up until the Telstar introduced the 32-panel, pentagon-and-hexagon stitching pattern, but it appears to me that remained unchanged for almost 40 years, from 1970 to 2006. The balls in between appear to have the same stitching pattern, just different printed designs.

• #### And it can't be unseen... (Score:1)

by Anonymous Coward

Best mockery of the 2014 World Cup logo - EVER!

Also quite accurate for the Brazil-Germany, errr, match.

• #### FOOTBALL... NOT "SOCCER"!!! (Score:1, Insightful)

by Anonymous Coward

The game is called FOOTBALL, not "soccer". Now that you -in the USA (you were good enough in the Mundial, as my national team Greece was, congratulations)- start to learn about it and realize that it's played mostly with the ball in the foot... stop calling your rugby "football" (change it to something like, e.g., American rugby) and start calling football by it's name: FOOTBALL
(and it's time to adopt the metric system...)

• #### Re: (Score:2, Troll)

Different languages use different words. Get over it.
• #### Re: (Score:1)

Football can mean either Rugby or Soccer. Since Rugby is short for Rugby Football, and Soccer is short for Association Football.

• #### Bra Bazooka? (Score:2)

Damn, I was hoping this was about a bra bazooka.
• #### Chemcially feasible? (Score:2)

I can't see those 8 member flat rings being at all chemically feasible. I really don't think this is possible to make as a carbon molecule.

Aromatic rings need to have 6 or 10 electrons in the delocalised orbitals, so an 8 member ring is going to need to have some other elements/groups to be at all stable...

• #### Re: (Score:1)

The rings themselves are perfectly reasonable (Cyclooctatetraene) non-aromatic hydrocarbons. Stitching together the mosaic the mathematicians propose is some serious work to be sure though.
• #### Re:Chemcially feasible? (Score:4, Interesting)

on Thursday July 10, 2014 @11:09AM (#47424753)

Yeah, you can make the ring, but how do you get it to be flat so they will fit into a sphere?

• #### Re: (Score:1)

The flat conformer is a simple transition state so I would imagine a catalysis kind of approach where you shift the energetics around as you stitch things would be one way. Then again I am not a bench chemist so there are probably many strategies for that which I know nothing about.
• #### Re: (Score:2)

I really with I could follow this part better ... it sounds like you guys are the only ones talking about the chemistry, and that's the part that I'm most baffled by. :-P

• #### 'Soccer ball'! (Score:1)

The article quite correctly calls the ball a football and never mentions the word 'soccer'.
• #### Re: (Score:2)

But a football is the ball used to play Gaelic. A soccer ball is what you use to play soccer.

• #### Is it too much to ask... (Score:5, Insightful)

on Thursday July 10, 2014 @10:52AM (#47424653)

In an article about a breakthrough in molecular topology, I'm currently seeing, while browsing at 2,

-7 comments about the relative merits of the soccer balls that inspired this discovery,
-6 comments condemning sports fans in general and soccer ball buyers in particular,
-4 comments whining about the fact that the U.S. doesn't have the same regional dialect as the commenter,
-1 terrible almost-pun,
-1 comment that is completely incoherent and incomprehensible,

and a grand total of 1 comment about molecular topology. Is is too much to ask that we could have some comments from posters who are interested in, you know, math and science? Here I was getting ready to dredge up all that symmetry and topology that got drilled in to me in grad school. Oh well.

• #### Re: (Score:1)

Maybe Slashdot could use an on/off topic moderation level.

(I wasn't going to post on the subject, but now I can write an off topic post too :-)

• #### Re: (Score:2)

Is is too much to ask that we could have some comments from posters who are interested in, you know, math and science?

I'm sure many of us are interested, but seriously out of our depth on the topic -- I don't even know what stupid questions to ask first without sounding even more stupid. :-P

I have no idea of what this actually means in terms of anything practical.

Here I was getting ready to dredge up all that symmetry and topology that got drilled in to me in grad school.

By all means, bust it out .. because

• #### Innovation is bad? (Score:1)

I can appreciate that being a US-based board, /. isn't filled with soccer fans, but still, why all the poo-pooing on innovation? Does the newest iPod really do anything predominantly different than its predecessors? How about that Galaxy V versus the III? Saying the Brazuca and Telestar are the same is like equating the 15-inch CRT that came with your Hewlett-Packard to the current 32" flatscreen you're sitting in front of. They both let you see what your surfing, right?

As a fan and recreational player
• #### And that means? (Score:2)

But here's question that has been puzzling chemists, topologists and..errr...soccer fans: is there a molecular analogue of the Brazuca?

OK ... so mathematicians proved you could have molecules with a symmetry similar to a new fangled soccer ball.

Is this good? Is it not good? Is it useful in any way? Or it this purely an intellectual exercise?

I'm afraid I don't grok chemistry with fullness, so I don't know if different symmetries give us different materials, or prettier chemicals.

I know shape usually defin

• #### Re: (Score:1)

by Anonymous Coward

The science gives people something to think about while watching another boring 0-0 soccer game.

• #### Nuclear weapons (Score:2)

I wonder if any of these shapes are found in the pit of modern nuclear weapons.

IIRC reading about the Fat Man devices the explosives/lenses were the shape of a conventional soccer ball, which as it turns out is sub-optimal.

• #### Irony (Score:1)

Goldman Sachs Predicts Brazil As World Cup Winner http://blogs.wsj.com/moneybeat... [wsj.com]
• #### Coincidence (Score:1)

Yesterday was also the 52nd anniversary of the launch of the Telstar-1, the world's first active telecom satellite, the world's first privately-ventured space-faring mission and first commercial payload into space. http://www.nasa.gov/topics/tec... [nasa.gov] PS: Does anybody else find it weird that Telstar and Death Star not only are phonetically similar, but look eerily so as well?

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