Carrying your stuff in a piece of textile has very long history, heroes of Russian folklore tales do so, and contemporary authors, Yuri Norstein and Sergei Kozlov in 1975 animated film "Hedgehog in the Fog" (on the picture) use this as a method to demonstrate simple life of forest creatures.
In Japan hirazutsumi meaning "wrapping cloth", or Furoshiki is an art of bending and twisting a piece of fabric to use it as a bag. But the general idea of ours will be to make something like paper bag, but from more strong and longlife material.
I will make a shopping bag from used advertising poster, it is very durable mesh fabric, impregnated with molten plastic.
Fabric, scissors, measure tape, stapler, glue, straps
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Step 1: Parametrization and Scheme
In the beginning I calculate its PARAMETERS, it will be the simplest rectangular form with three dimensions a×b (bottom) ×h (height). And according to this I cut my flap (a+2b × 2h+b). And then I should bend it the proper way: black dash lines show fold lines (and recommended order), in which internal side of material is pressed together, and the blue lines show last folds, where outside is pressed face to face.
Step 2: Assemble Sides
Now I staple together with ordinary office stapler the future double sides at upper end.
Step 3: Assembly Inner Corners
Push all bended sideline within the bag and press to bottom, and the lower part of an outside piece is bended first, until it forms a triangle in the bottom, and the same to the second, internal part of a side, until it forms smaller triangle in the bottom, and this small triangle I staple few times too. The same for the other side.
Step 4: Handles
And the handles too, they are from used polypropylene packaging strapping tape.
Step 5: Glue
Now it is strong enough by itself, say, for presents and decorative purposes, but for shopping I'll fasten it all with liquid nails.