Dodecahedron from Bike Rims

 

1. Progress to date - 3 rims drilled, and 3 edge joiners made.

2. Detail of rims joined and drilled. Joiner is ......

3. this which is a piece of 25mm round dowel timber. Surrounding it in black is a drilling jig which ensures holes through are correctly positioned.

4. Dowel cutting. There are 30 connectors to be cut so this setup was worth it to cut quickly and accurately. Plastic pipe is another option but I wasn't sure about cutting it with this setup.

5. Typical source of rims. This is a discarded De Carlo bike with the 27" steel rims used in this project. Its resto is documented here. The now-installed 700c aluminium-rimmed wheels are lighter, easier to get parts for, and brake better the the old 27's.

6. Layout diagram for wheel drilling and drilling jig shown in 2.

Hi Good progress on this project in the last few days. I have been thinking about it for ages and finally got working on it a few days ago, after gathering enough wheels and buying some dowel to make the edge joiners from. Principles to make this sort of thing are outlined in my article for the Australian Mathematics Education Journal which is here (official site) and here (full version through researchgate). Also, this post describes building the same thing in beer cans!

Basically, any old circle can be made into a polygon (pentagons shown here) , and from there into a platonic solid outline (dodecahedron started here). 

The rims I am using are mostly 36 spoked / holed, which is not divisible by 5. This means some extra drilling has to be done, and I worked out a diagram for the drilling, which is not too hard.

Another donor vehicle. This Apollo bike has frame damage at the head tube and so is being ripped apart. I will take its frame to the recycle depot soon.

All the wooden dowel pieces have been drilled and varnished now, and this was the drilling setup. The jig stays in the vice, then the dowel is inserted and drilled. Quite quick.

Rims have all been despoked, and I've numbered the spoke holes so I know where to drill.

The top rim in this shot has been drilled, the rest are marked up.

Update 2/1/2023: Happy New Year!  And hi ho, its back to work we go.  Quite close to finishing now, I've extracted all the 27" rims I need, and just need to drill 9 of them with 5 equispaced holes before assembly can start. Quiet time in Melbourne, I went for a 7am swim in the yarra which was nice. 28 degrees C already, quite warm.

Assembly while watching "Rivers" on the TV. If it was all put together, it would be too big to get outside.

All the bits

Centrepunch done, drilling follows next.

22mm spacing markup

11mm spacing markup. A spoke nipple is used to make a centre point for one leg of the dividers.

 11pm update!

Close to finishing now. I smashed through some rim marking up, rim centre punching and rim drilling this evening so I could start assembly. About 1/2 of that is done but I came across a drilling mistake, and will fix that and keep assembling tomorrow.

 

Update 3/1/2023 Finished now!  It was just as well I stopped last night as there were 2 drilling mistakes that needed correcting. Today I've drilled holes in the correct spots in 2 of the rims, assembled half-sections inside, then assembled the 2 halves of the dodecahedron outside. 

I kept a lot of the screws loose until the last screw was in, which was just as well, as there was a bit of a fight to get the last screw in. Properly marking out the first 3 rims might have helped.

The selfie photo was a bit of a challenge, as there is a 12s time gap from pressing the button on the camera to the photo being taken. During that time I needed to slither my 62 year old body into the thing. I tried this twice and banged my head on it on the 2nd attempt!

As you can see the back garden is a bit crowded with moderately sized bike rim sculptures, and the tetrahedrons will have to go!  The big tetrahedron folds flat at least! It is described in previous posts here and here. Very glad my late wife Chistine got a laugh out of it!

 Update Jan 4

Overnight I did some calcs on how big the dowels have to be on platonic solid structures like the one I've made, and the results are shown above. The size depends on the shape concerned (due to its dihedral angle ) and  the rim width and geometry. My dowels seem to be undersize, but I think because of the rim rounding I got away with it.

The last pic shows a modest sketch of what's next, or what could be next. I've already established that 3 rims can be bolted together to make a larger side, and by putting 15 sides together, a part icosahedron could be made. this could be a good greenhouse or cubby house or chillout tent. Even larger would be a 6-rim-per side part icosahedron.

Regards  Steve Nurse