I've been trying to memorise the folding sequence of some traditional models and in particular the 'lover's knot' diagrammed here by David Petty.
It has a very pleasing final step which 'knots' the paper so that it cannot be easily undone. As you can see it also produces 6 points or tabs, some of which can be opened into pockets.
This could make a great module I thought, so I folded 2 knots from the same size paper and started to look at how they could connect with each other. Several ways became apparent but this one seemed to offer more possibilities, at 90 degrees and with a very firm connection: The point of one covers the other and when pushed follows its line, finishing at the centre of the central square:
With more added, this little beauty emerged:
Different colour combinations at the joining point are possible with this 2 tone example if you vary which tab goes into which pocket.
Very pleased with the result, I then thought about using the units to create a polyhedron: The join is at 90 degrees so a cube should be possible. So 24 freshly folded units later and a lot of fumbling produced this:
Connecting the last face of a cube was quite a struggle. If you're tempted to push your finger through the central square where the 4 loose points meet, it becomes a finger trap!!
Two extra mountain folds are inflicted on the knots where the points bend over to the adjacent 2 sides but they can be soft folds which gives a somewhat puffy appearance to the cube and this way the integrity of the original model isn't really lost.
If you don't mind about this sort of thing you can also push those loose points all the way back into the corners inside the model like this:
Can anyone think of any other model in origami which can be used as a unit in this way without any modification?