## Friday, July 26, 2013

### Origami Buckyball Puzzle

Challenge: Make a Origami Buckyball ( A dodecahedron - 20 vertices, 30 edges, 12 faces (regular pentagons)) using three colors so that no two units of the same color touch.

I love puzzles and this challenge took me a few hours to solve. In order to solve this puzzle, I had to do a little exploration of the materials.  Given three different colors that meet at a point...how many combinations can there be.  As you can see from the photo below, only two.

The next problem was combining these pieces to create a pentagon.  How many different combinations are there?  Three combinations.

The final problem is how to put these pentagons together to create the dodecahedron, where all vertices are different colors and don't touch one another. After trying a few combinations, I discovered that I needed more theory.  It is a circuit problem.  A Hamilton Circuit in particular.

Starting at a point in the middle.  You need to draw a line so that you do not lift your pencil.  This creates a circuit.

Next you need to alternate the colors of the line. Notice that each vertex has three lines emanating from it and that there are three different colors.  Yes...problem solved!

The final result.

I cut out the 30 squares using my Cameo Silhouette.  I am not including the cutting file because it is so easy to make a 3 inch square and fill a page.  Here is the origami directions for making this Buckyball http://www.nisenet.org/sites/default/files/catalog/uploads/9728/buckyballorigamiv02.pdf

#Hamiltonian circuit #Origami puzzle #Cameo Silhouette