plaiting instructions for Dodecahedron, Icosahedron (vertex-plaiting), small stellated Dodecahedron, great Dodecahedron, stellated Icosahedron.
(may be neglected, every way of plaiting the paper strips obeying the plaiting principle should work)

notation:
I, II,.., VI: the 6 paper strips;
a1, a2,.., a5: the 5 outer quadrilaterals of a strip; i1, i2,.., i5: the 5 inner quadrilaterals of a strip;
↑↑: place upon in equal orientation, ↑↓: place upon in reverse orientation

plaiting actions:
1) i3II ↑↑ a3I;
2)
i3III ↑↑ a3II, i4I ↑↓ a2III;
3)
i3IV ↑↑ a3III, i4II ↑↓ a2IV;
4)
i3V ↑↑ a3IV, i4III ↑↓ a2V, i3I ↑↑ a3V, i4V ↑↓ a2II, i4IV ↑↓ a2I;
now plait in strip VI:
5) i2I ↑↑ a2VI, i2VI ↑↑ a4III, i2V ↑↑ a1VI, i1VI ↑↑ a4II, i2IV ↑↑ firstVI, i5III ↑↓ a1I, i3VI ↑↑ a4IV, i2II ↑↓ a3 VI, i5IV ↑↓ a1II, i4VI ↑↑ a4V, i2III ↑↓ a4VI, i5V ↑↓ a1III, i1III ↑↑ a5IV, i1II ↑↓ a5III ↑↑ firstIII, eIII under a5IV, i5VI ↑↑ a4I, i5II ↑↓ a1V, etc., apply the plaiting principle to finish.

fastening of the end-quadrilaterals:
the quadrilateral marked "e" (end) of every strip always has to be fastened under some other strip and it always has to be placed on a "first" quadrilateral of a certain strip. When fastening of a whole "e"-quadrilateral seems too difficult, it should be folded first to obtain a triangle, which can be fastened more easily.

 i1 a1 i2 a2 i3 a3 i4 a4 i5 a5 e I ↑↑i1V ↑↑a5II ↑↓i5III ↑↑a2VI ↑↓i4IV ↑↑a3V ↑↑i3II ↑↓a2III ↑↑i5VI ↑↓a1IV ↑↑i1V ↑↑a5II II ↑↑i1I ↑↑a5III ↑↓i5IV ↑↑a3VI ↑↓i4V ↑↑a3I ↑↑i3III ↑↓a2IV ↑↑i1VI ↑↓a1V ↑↑i1I ↑↑a5III III ↑↑i1II ↑↑a5IV ↑↓i5V ↑↑a4VI ↑↓i4I ↑↑a3II ↑↑i3IV ↑↓a2V ↑↑i2VI ↑↓a1I ↑↑i1II ↑↑a5IV IV ↑↑i1III ↑↑a5V ↑↓i5I ↑↑a5VI ↑↓i4II ↑↑a3III ↑↑i3V ↑↓a2I ↑↑i3VI ↑↓a1II ↑↑i1III ↑↑a5V V ↑↑i1IV ↑↑a5I ↑↓i5II ↑↑a1VI ↑↓i4III ↑↑a3IV ↑↑i3I ↑↓a2II ↑↑i4VI ↑↓a1III ↑↑i1IV ↑↑a5I VI ↑↑i2IV ↑↑a4II ↑↑i2V ↑↑a4III ↑↑i2I ↑↑a4IV ↑↑i2II ↑↑a4V ↑↑i2III ↑↑a4I ↑↑i2IV ↑↑a4II