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My icosahedron got stuff stacked on top of it 😡😡 so I had to reconstruct it, and some of the straws are permanently bent, but here's a 5-way vertex that still looks pretty good. As you can see you can extend this method almost indefinitely, in any direction, at the expense of a slightly larger vertex. I've also made a hypercube and some of the joints have straws going in every direction. But that also got stuff stacked on top of it 😡😡😡, so there's nothing to photograph right now. But try it! You'll see how it works once you get going, and it's really easy.
If A B and C all meet at a vertex, join A to B, B to C, and C to A.
Therefore no joint has more than two straws.
Another, super easy method of joining straws is to use another straw. Crease along the long axis and then fold in half along the short. Insert into two adjacent straws. Each open straw end can accept two folded straw connectors, which provides enough friction to hold them together. Easy, and easy to reconfigure. I've made icosahedrons, dodecahedrons, and hypercubes this way.
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