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Here the folding lines are not diagonals of the outer/inner quadrangles of the paper strips; the cube is "(2|1)-wrapped", see:   http://www2.eng.cam.ac.uk/~sdg/preprint/weaving.pdf
Cube platonic solid 8 vertices 12 edges 6 faces 6 squares (6 sq.)		"(2|1) wrapping" 6 strips 10 x 1/5 sq.	pattern download, 6 paper strips 2641 x 1413 pix, 312 kb, w21.jpg
plaiting scheme: a1 a2 a3 a4 a5 I ↑↑i4V ↑↓i3II ↑↓i3IV ↑↓i1V ↑↑i5II II ↑↑i4VI ↑↓i3III ↑↓i3V ↑↓i1VI ↑↑i5III III ↑↑i4IV ↑↓i3I ↑↓i3VI ↑↓i1IV ↑↑i5I IV ↑↑i5V ↑↓i2II ↑↓i2V ↑↑i4II ↑↓i1I V ↑↑i5VI ↑↓i2III ↑↓i2VI ↑↑i4III ↑↓i1II VI ↑↑i5IV ↑↓i2I ↑↓i2IV ↑↑i4I ↑↓i1III
Cube platonic solid 8 vertices 12 edges 6 faces 6 squares (6 sq.)		"(2|2) wrapping" 8 strips 12 x 1/8 Q.	pattern download, 8 paper strips 2787 x 1723 pix, 171 kb, w22.gif
plaiting scheme: ↑↑ a1 a2 a3 a4 a5 a6 I i3IV i2III i1II i2VIII i1VII i4VI II i3VIII i2VII i1I i2IV i1III i4V III i5V i4VIII i3II i6I i1IV i2VI IV i3VI i6V i3III i2II i5I i6VII V i5III i6IV i1VI i4VII i5VIII i4II VI i5VII i6VIII i1V i4III i5IV i4I VII i5VI i4IV i3I i6II i1VIII i2V VIII i3V i6VI i3VII i2I i5II i6III

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