Is there an easier way to make a polyhedron with hexagons and pentagons?

[meepmeep90]

I am trying to make polyhedron with hexagons and pentagons and I am struggling to find a way to "merge the edges" or bring the shapes together upward to form a 3d shape. I started with a hexagon, and then 3 pentagons + 3 more hexagons with the same side length and rotated them to the correct spots. 

I want to do it with math, which I assume is the correct way but if there is a snapping or aligning method that would be easier I am all ears! Thanks in advance 

[jhackney1972 · Accepted solution]

A soccer ball is constructed the same way.  I used two components and a bunch of assembly joints.  If you slide the timeline back two steps, you will see the rough shape.  Model is attached.

[meepmeep90]

Your model and explanation were MOST HELPFUL! THANK YOU I was able to get them working once I figured out they needed to be revolute hinges. MUCH appreciated