Lovers Knot goes modular

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?

The Butterfly Effect

I mentioned a "Butterfly" lock in my last post but don't remember ever seeing the move explained as a technique in any origami book so you may be unfamiliar with it, or perhaps just know it without naming it.

Difficult to explain in words, a sort of a 'crimp' combined with a 'sink' - here is a diagram.

So in this example a fish base is collapsed along both diagonals with two of the creases reversed all in one step. When complete the model should look like the stylised butterfly photographed above. It could of course be collapsed in a mirror image with the flap inside pointing the other way.

There are 2 other models I can think of which use this move to great effect:

• Sharon Turvey's 'Flower with Stem' diagrammed in BOS magazine 257 (step 9). I remember she made us laugh when she taught it to a group of us at a recent BOS convention by starting her instructions with the words: "Book, book, nappy, nappy, blintz, blintz..."


• Chan Yew Meng's "Four Leafed Dish" diagrammed in the Winchester 2009 BOS Convention Pack This clever model uses the technique to form a simple open bowl where 4 butterflies are joined with their lower tips meeting in the middle of the base like a Masu box.

Would love to hear if you know any other models which use this technique.

Earthstar

I came up with this model while doodling with a windmill base. It's fully 3 dimensional as you can see from this back view.

The folding sequence includes 4 'butterfly' locks which create a cone shape. There is something strangely satisfying about a butterfly lock (maybe I should get out more!): you make a few creases, fold the edge to the centre incorporating a crimp and you have an instant neat 3D model.

This is a fairly simple design so can be made from all sizes (the ones pictured are from 8.5cm to 15cm squares) and all types of paper even thin magazine pages . I found it difficult to decide what to do with the triangular flaps which cover the centre. I finally decided to curve them upwards and inwards to give the impression of a split seed pod.


The fact that it originated from a doodle and is not a deliberate attempt to imitate Nature made it difficult to choose a name for the model but I stumbled across a picture of a curious looking fungus called an earthstar and although not entirely similar the name has a good ring to it so "Earthstar" it is.