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