The tutorial is for the subunit of the cube, but the principle is the same for the icosahedron; the triangular central element is replaced by a square or pentagon as required to provide four or five spokes.
See "Sphere of Curved Struts" http://www.dotpedia.com/creations/view/967 for detail on how to make the curved struts
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see the video on how to make the smallest one (with a 3ring in the centre). The subunit has polarity, but can be joined upside down and interlaced as well as the way shown. Each is shown unfolded and then folded (below). The extra ring on one of the spokes has the same number of spheres as the centre ring.
Here are two sorts of curved struts (one sort (bottom left) is used in "large icosohedron" shown below). They are shown in the flat state and the folded up curved state. To the left is an example of one way to join them up with the other subunit.
The curved strut on the top has a tighter curvature.
see also "Sphere of Curved Struts" http://www.dotpedia.com/creations/view/967 for detail on how to make the curved struts
This is actually a cube, albeit with curved sides.