So coil the string up to make a 5-sided shape as shown and make 12. Then put them together either dished-side-in (to make a dodecahedron) or dished-side-out (to make an icosahedron). They should join square ball-to-ball; if they misjoin ball-to-space-between-balls then one of them is dished the wrong way. Then just disassemble and flip one though itself, turn it over and reassemble. For the icosahedron put a single ball in the hole in the middle of each pentagon after assembly.
The icosahedron has pretty flat sides whereas the dodecahedron is hollowed - but still looks good! Obviously the icosahedron has 12 vertices to the dodecahedron's 12 sides - but I am sure you knew that!
