Folding Stellated Icosahedron
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This icosahedron prints with faces flat along the print bed, then folds along every edge to assume a 3D shape.
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This model works just like the Dodecahdron it is remixed from, though it is necessarily a bit smaller to be able to fit 20 faces flat on the print bed. Once printed, the shape folds along each edge to the dihedral angle for a regular icosahedron. You can hold the sides together (except the last one) by securing them with 2mm wide zip-ties through the holes as shown in the picture. For the last fold, I used thin enameled wire pulled through connecting holes to pull the two halves together along the last fold and secure them.
Print in PETG with .2mm layer height. The edges between faces are designed to be 2 layers thick. It's possible to print with PLA, but when I tried it, I found that the edges would break after being flexed a dozen or so times while I was trying to insert the LED string. PETG is much sturdier and more flexible. If you plan to just fold and secure it once, you can probably get away with PLA.
If you use translucent filament, the print looks very nice illuminated by LEDs, as the video at this link shows. A flexible LED string like this one, works well. The zip ties holding the sides together can be used to hold an LED string in place.