You can make balls from strips of any material that has the right combination of stiffness and flexibility, like stiffened fabric, chair cane (soak it first), plastic sheet or the veneer strips meant for edging furniture. My next task will be to weave a lampshade from some plastic post-factory waste strips that are (I think) polypropylene and came from the Leeds Scrap Warehouse.
The weaving process is a little tricky, so I suggest you start by making a ball from paper to get used to the technique. An A4 sheet (297 mm x 210 mm) will make a ball that is about 85 mm diameter, because each 297 mm long strip goes right round the circumference. Therefore, allowing 7 mm for the overlap where the ends meet, d=290/π or 92 mm. (It will be a little smaller because some of the length of the strip is taken up in weaving in and out.)
Balls like this made from plain coloured paper or Christmas wrapping paper would make pretty tree decorations. You can make a bigger ball if you like, but don’t try a smaller one until you know what you’re doing, it will be too fiddly.
Whatever size of ball you want to make, the strips you use should have an aspect ratio (width:length) of somewhere around about 1:35 or 1:40. You can use a bigger ratio (eg. 1:50) to produce a more open ball, but a ratio that is much less than 1:35 won’t work. Note that the dimensions for an A4 paper ball are different, because each strip is folded lengthwise into 3 and only then is the ratio about 1:40. If you use something that is stiffer than ordinary copier paper, then it will not be necessary to fold it into 3, or possibly not even into 2. Making a small paper ball as a test piece before trying anything more complicated will help you to understand what degree of stiffness is required – too stiff and it will be impossible to weave, too floppy and the ball will not hold its shape.
Fabric can be stiffened by painting on diluted PVA (a ratio of 4 parts water to 1 of PVA is suitable) or using spray starch. If using PVA, allow it to dry and then paint on another coat if it isn’t stiff enough. Cut the strips after stiffening to minimise fraying.
Materials for an 85mm diameter paper ball
A sheet of A4 paper (approx. 80g/m2 – ordinary printer/copier paper) or a larger sheet of paper sufficient to cut 10 strips that are each 297 mm long by 21 mm wide
10 or so paperclips
Masking tape or sellotape
A pencil and a ruler
Scissors or a craft knife or roller cutter and a cutting mat