Geodesics!

My initial blog creation has sadly been followed up with...not much! See if I can turn that around...

Today, my mind has been on faceted spheres.  This is a ubject that has interested me since I was 11 or 12, and saw a PBS special on buckminster fullerenes (or bucky balls!).  These are the molecules with the formula C60 which resemble a soccer ball, with the facets formed by the carbon molecules making up 20 hexagons and 12 pentagons.   After watching it on TV, I had to "try it myself,"  and got out the scissors and paper to make my own--which I did with some success, though it was a bit floppy.

http://en.wikipedia.org/wiki/File:Buckminsterfullerene-perspective-3D-balls.png

Bucky balls were named after Buckminster Fuller, an architect and designer who popularized geodesic domes in the 1960s, with impressive structures such as the Montreal Biodome and the huge sphere at EPCOT.  The geometry of the geodesic dome can be created by taking a regular icosohedron and subdividing its facets into triangles.

Virus capsid are regular icosohedrons!

Geodesic sphere from  http://www.vb-helper.com/howto_geodesic_sphere.html

 Then, if you take the "dual" of the geodesic sphere, you get a bucky ball.  This means, if you connect the center points of each facet of the sphere with a line segment, the resulting shape (made up of the new segments) would be a soccer ball/bucky ball.  Kinda cool!  What's really interesting is, if you take the dual of the soccer ball, you get another soccer ball... with an increased number of hexagons, but still with 12 pentagons.  This can be repeated to get a more and more complex sphere, composed mostly of hexagons...but still with 12 pentagons!  It seems geometry prevents a true all-hexagon polyhedra.


See if you can find the pentagons :)

On the other hand, the "hexagon sphere" pictured here is LIE:
http://djjarak.deviantart.com/art/Rainbow-Hexagon-Sphere-319793632
No pentagons!

All of this brought me to an idea for a potentially time-consuming DIY project.  A Catan globe!

http://settlers-of-catan.blogspot.com/2010/08/seafarers-of-catan-fog-island-for-four.html

If you're not familiar, settlers of catan is a board game, with the board made up of interchangeable hexagons representing different types of terrain.  It's pretty great, kind of a cross between monopoly and Risk, but less cut-throat since the goal is to be the first to create a little "civilization" worth 10 points rather than stomping out your opponents.

So... Could I play this on a geodesic globe?  Maybe something like this?
http://sourceforge.net/projects/hexmapsphere/

or this?
 http://www.ucar.edu/communications/quarterly/spring09/latitude.jsp

My globe would have a lot less facets than these examples, but it would still be a big project.  The game pieces might need some help to stay attached.  I'm thinking magnets.  A basic frame could probably be created by hand from posterboard, and laser-cut plastic facets glued into place.  Will this become reality?  Probably not..but its fun to think about...

Some other interesting (to me!) related links:

http://www.georgehart.com/virtual-polyhedra/turnings.html  =oldschool hand carved polyhedra
http://www.saintjohnsabbey.org/wenninger/index.html =Benedictine monk making polyhedra origami
http://www.bugman123.com/index.html =my new nerdy hero