The Elusive Icosahedron

[Ps 27:1]

The fact that there are exactly 5 platonic solids should intrigue anyone with a mathematcal bent.

This puzzle has to do with the 5th, the icosahedron. http://en.wikipedia.org/wiki/Icosahedron

It has 20 faces, 12 vertices, and 30 edges. How can you show a person with at least an 8th grade education (certain states exempted) that the icosahedron has 30 edges in just a second or two.

Restrictions:

1) No counting of individual edges. (would take too long)
2) No Euler's formula V - E + F = 2. This is 8th grade and below.
3) No telling directly like writing the number 30 or saying "30"
4) They have to see it themselves and you can tell them ahead of time what they are looking for. But when you present the icosahedron to them, they should be able to tell it's 30 within a couple of seconds.

This can be a very hard puzzle. Much harder than the 0 in the cube. But!!! When you see the solution, you will see that it is also very simple and everyone that has had a proper education to about the 8th grade (maybe even less, I'm not sure) can see and agree with the solution. Richard, I think you will really like this one.

So what separates it from being hard and easy? Revelation and experience.

There's a metaphor in there somewhere.

Steve

[Ps 27:1]

Just like the solution to the magic square riddle, this puzzle is solved by using the next dimension. I don't have any magnetix with me so I combed youtube to see if anyone had this. I know some of my students posted pictures and/or videos to facebook, but I never saw them.

You have to spin the icosahedron so that it can "show" you the answer.



I have no idea who this guy is and he never catches the image made in the center. Bummer!

You have to look at it straight on and you will see [X X X] plain as day. All my students could see it. And, of course, you need to know that XXX is Roman numeral for 30, hence the 8th grade education.

It is actually pretty cool, and most of the students loved creating it and others and spinning them to see whatever. Nobody showed me this optical ilusion, I just discovered it one day from playing with the magnetix.

Cheers,
Steve