Truncated icosahedron

Introduction

The geometrical shape of this ball is called truncated icosahedron, but you may also know it as a football/soccer ball or bucky ball. The ball is not very strong. It holds together pretty well, but it cannot take a lot of stress. It even changes shape somewhat under it’s own weight. My plan was to make a ball with a mechanism inside to make it roll, but this ball is not strong enough for that. However, since I like the looks of it and since it demonstrates the structure of the truncated icosahedron quite well, I decided to display it separately.

The color scheme of the digital design is slightly different from the pictures. The difference is in the color of the hinges. I imagine that different color schemes look good as well.

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Building the model

Download the design in Ldraw here. I made it on a Mac with Bricksmith, but the file should work with other Ldraw software too.

Just a few pointers to help you build it.

  1. First build the flat versions of the top and bottom halves of the ball according to the Ldraw design. You will notice that it is quite flexible and that the hexagons and pentagons can change shape easily. The two halves are similar, but not exactly the same and also not each other’s exact opposite!
  2. In each half, start connecting the hinges that are not connected in the design from the inside out. I.e. start with the hinges on the inner ring, then all the hinges on the outer ring. In this process, the hexagons and pentagons will take their shape more clearly and the half-ball takes it shape. The more the half-ball takes shape, the easier it is to connect the hinges.
  3. Set the two halves on top of each other and connect the hinges between them.

Instead of the axle pin long (part number 11214) you could also use regular axle pins and friction pins.

Reinforcing and Up-scaling

Elements loose shape

A quick look at how the hexagon and pentagons are shaped, suggests that it is easy to scale up: just use longer bars. I have not done it myself, but I am guessing that you’ll have two problems to solve. You’ll need two or perhaps three or more hinges per edge. Secondly, I longer bars and more hinge parts will make the ball heavier, which means it may become so heavy that it will not keep its shape very well.

Most of the loss of shape is caused by the fact that the hexagons and pentagons are flexible. So to prevent that from happening, they need reinforcing. I have found three solutions, none of which are completely satisfying.

The one to the left and the one in the middle keep their shape better than the one to the right. The one to the right can hold pressure on opposite sides and opposite corners, but looses some shape when pressure is put on two corners that are not neighbors and not exact opposites. When applied in a rolling ball, I hope but am not sure that such pressures do not occur.

The solution to the left does not give enough place for the hinges, unless the spokes are turned to the outside of the ball. However, I am not sure what it does to the rolling qualities of the ball. The solution in the middle allows space for the hinges, but since the walls are three bars high, the hexagons may stick out too much.

The solution to the right is somewhat less sturdy than the other two but the hinges can easily be applied to the edges and the walls are only two bars high. So for the next version, I would opt for this one.

A final remark about all solutions : they can only be implemented on the hexagons, but not on the pentagons. The symmetry of the pentagons seems not to allow any reinforcement. At least, I could not think of any. Perhaps this is not a problem. All pentagons are surrounded by hexagons, so those hexagons may provide enough stiffness for the ball to keep its shape.

 

Different walls

Wall design v1

For no particular reason, I ended up having the sides of the hexagons and pentagons made of 7L bars (bars of 7 pin holes). One wall would look like this image.

Because of this, the hexagons had to have  two bars sticking out with one hole. A more elegant solution would be to have the sides 8 pin-holes long. Then one wall could be made like this:

Wall design v2

 

Hexagons and pentagons would then be made in the same way.

 

Popping knee hinges

During the build and when applying pressure to the ball, the hinges at the corners of the pentagons and hexagons may let go. They consist of simple pins, and especially used pins that have lost some of their strength easily snap loose. A stronger solution would be to add a third bar.

Wall design v3

The hinge still consists of one pin, but since there can be multiple pins to hold the third bar in place, the hinge will be able to withstand a lot more pressure.

A possible downside of this solution is that a wall element becomes three elements high and stick out too much. I.e. the distance between the hinges that connect the edges and the outside bar be so high that the wall parts have difficulties with side-way pressures when the ball rolls. I am not sure this is the case since I have not (yet) tested it.

I have tried to move the hinges from the bottom position on the wall to middle position but this requires many parts. Moreover, the hinges need to stick out further from the wall to prevent walls of different hexagons from being in each other’s way. It means that the distance between the hexagons becomes 3L instead of 1L, but perhaps that is less of problem than I imagine. It just does not look nice.

 

Holding shape and stronger knee hinges

Combining the solutions to the loss of element shape and the popping knee hinges seems problematic. Two of the solutions to prevent the loss of shape connect with a pin to the knee hinges. This can be done with the two-bar walls of the current design but not with the three-bar walls for stronger knee-hinges. Or at least, it can not be done in an elegant way, since there are no 4L pins. Possibly, it can be solved with a 4L or 5L axle with a stop.

I tried to combine wall design v2 (with 7L bars) with the right most design for reinforcement, but could not get it to work. It can probably be done with 9L bars, but I have not tried it. The walls will then be 10L long which means the ball will become a lot bigger than the one presented here, which has 7L walls.