Joiners to construct a buckyball from sticks or tubes.
A buckyball only needs one kind of joiner and one kind of rod.
Two sizes are posted here. One takes 6mm rods and one takes 3mm.
The parts could be scaled up to make large structures but it would be an expensive exercise.
A complete set of 60 3mm joiners needs about 100 grams of plastic.
Printed at .4mm layers they take about 5 minutes each.
For 6mm parts multiply that by a factor of eight.
For 12mm multiply by eight again.
A set of 3mm might cost $3 - 6mm $24, 12mm - $190 and 24mm $1500.

I posted the joiners in pairs to improve packing when printing many at once. Each joiner in at the junction of two hexagons and one pentagon.
The orientation of the joiner must be correct to form the ball. It would not be obvious which way is correct so I've add some guides.
There is an arrow on the bottom which point to the pentagon. The arrow can be hard to see on some prints so I also added a little pointer to the perimeter of the base.
I've printed them at both .4 and .2mm - both work.
Prints at .2mm look a little better but it probably isn't worth the extra time.
I'm printing the 3mm parts 12 at once. The print bed isn't full and I could probably double that,

The holes are cleaned up using a drill.
3mm OD bamboo skewers cut to length work fairly well with the 3mm joiner. Drinking straws work with the larger joiners but not good for anything meant to last.

I've also found they print OK at 3/4 scale and this is a good size for use with match sticks.

For mine I used skews cut to 100mm lengths. You could make them much longer or shorter as required.
The ball diameter is approximately 5 times the stick length
There are 90 stick so the total length of edges is about 18 times the diameter.

I've included a .stl of a ball for reference.

I think the easiest way to assemble in the start be turning the sticks and joiner into pentagons - make sure the arrow point in and the flats are all on the same side.
Then join the pentagons together with sticks. As long as no pentagons are flipped (ie flats on the wrong side) it should turn into a ball.