# Math Monday: Make a Ball of Money

By George Hart for the Museum of Mathematics

The diameters of US quarters and pennies are very close to the ratio needed to make a truncated icosahedron, i.e., a soccer ball in the US or a football elsewhere. Copper pennies take the place of the usually black pentagons and quarters take the place of the usually white hexagons, so even the colors work out. This ball was soldered together by Cory Poole.

Puzzle: Can you work out what it cost before looking at the answer found here?

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There are twelve pennies at the corners of an icosahedron, plus twenty quarters at the corners of a dodecahedron, totaling \$5.12.

### 24 Responses to Math Monday: Make a Ball of Money

1. Whoever mutilates, cuts, defaces, disfigures, or perforates, or
unites or cements together, or does any other thing to any bank bill,
draft, note, or other evidence of debt issued by any national banking
association, or Federal Reserve bank, or the Federal Reserve System,
with intent to render such bank bill, draft, note, or other evidence
of debt unfit to be reissued, shall be fined under this title or
imprisoned not more than six months, or both.

• It would still be fit to be reissued as you can easily unsolder it. If you read the full text of the actual law it uses the word fraudulently which implies that the intent has to be to defraud the government.  Also this law is regularly not enforced on coins as their are machines across the US in tourists places and gift shops that will press your money into a souvenir.   Needless to say I’m not too worried about the secret service coming after me…

• If I understand the mechanics of the economics right the government should be happy when people destroy coins and bills since that should reduce the inflation   Right?

2. There’s no intent to render it unfit to be reissued. I’ll take gladly take it in (partial) payment of anything I’m selling and issue change as required.

3. You can view a little more about this object and a few simpler ones (the platonic solids) here: http://oceananinchdeep.blogspot.com/2011/07/platonic-and-archimedean-solids-from.html

4. You can view a little more about this object and a few simpler ones (the platonic solids) here: http://oceananinchdeep.blogspot.com/2011/07/platonic-and-archimedean-solids-from.html

5. You can view a little more about this object and a few simpler ones (the platonic solids) here: http://oceananinchdeep.blogspot.com/2011/07/platonic-and-archimedean-solids-from.html

6. Gaspard Gazule on said:

Another rather close coin fitting property : http://www.flickr.com/photos/fdecomite/3155168703/

7. Eric Hearn on said:

OK, so. I tried soldering quarters together and they simply broke apart under their own weight. What did you do to keep this thing together?

• It was tough and I’m sure there is a much better way…  What I did was made a cardstock truncated icosahedron net and then cut away a lot of the unnecessary pieces so that I had a mesh with holes in it.  I superglued the coins to the polyhedral net and then soldered the pieces together.  This is a difficult proposition because the solder I used melts at about 400 degrees and paper burns at about 450!  Also I had to use a 250 watt soldering gun to have enough power to head so much connected mass.  Once all of them were soldered except one, I cut out and removed the net.  Solder or coldsolder (JB Weld) the top coin in place.  Note perhaps JB weld would be a better overall solution to this problem…

8. I’ve made birthday dodecahedrons with Sacagawea Golden dollars and “Coinstruction” connectors — see http://www.flickr.com/photos/tachyon/2211928525/ for the description, and http://www.flickr.com/photos/tachyon/2211928525/sizes/o/ for a picture large enough to actually see them.

Or here’s a golden-dollar/Coinstruction Pinhoe Egg stuffed with chocolate eggs: http://www.flickr.com/photos/tachyon/3355998714/

• Oooh cool.  I’ll have to look into these.  I clicked on the link for the coinstruction connectors and couldn’t find them but when I googled Coinstruction found places to buy them.  It seems to me that you should be able to build this structure with the connectors without any major problems.  It would change the ratios a bit but they seem like they would probably bend enough.

• The Coinstruction connectors are pretty stiff — while you can get a little flex there, if you’re trying to build something that uses angles other than multiples of 90° or 120° it can sometimes be tricky to get it to not just pull itself apart.

• The Coinstruction connectors are pretty stiff — while you can get a little flex there, if you’re trying to build something that uses angles other than multiples of 90° or 120° it can sometimes be tricky to get it to not just pull itself apart.

9. when i first made this shape i was surprised to realize that it is the same shape that is made when you make the rubik’s snake into the “ball”

one of my classes in college had us make a lot of basic solids leading up to this one. i believe the proper name for it is “rhombicuboctohedron” (scores a lot in scrabble)

10. when i first made this shape i was surprised to realize that it is the same shape that is made when you make the rubik’s snake into the “ball”

one of my classes in college had us make a lot of basic solids leading up to this one. i believe the proper name for it is “rhombicuboctohedron” (scores a lot in scrabble)