![]() My goal in this is to show how I went about using a little group theory to figure out how to use up my paper odds and ends. I'll focus on these, though the techniques apply to any polyhedron. Among Platonic solids, therefore, there are only three cases to consider. One consequence of this is that there is no distinction between solving the problem for a polyhedron and for its dual. Indeed, some modules leave holes in the centres of the faces, others fill them in, still others form stellations on those faces, but ultimately each module corresponds to an edge of the model. It can be useful at times to think of it as a wireframe model rather than a solid. So we are colouring the edges of a model. The other thing to get straight at the outset is that for most models the modules form the edges of the final polyhedron. Obviously to go back to the origami, we pick a paper design to correspond to each colour (though there is scope for a little more variation as the designs themselves may not be symmetrical on the paper). The goal is to allocate the designs so that there are as many "good" symmetries as possible 1.ġSometimes one wants to break the symmetry deliberately but to do this one needs to know what the symmetry is beforehand.Īlthough the motivating problem is of choosing paper designs for an origami model, the language I'm going to use is of colours because it makes for easier pictures. The symmetries of the model will interact with the choices, some in a good way and some not. The idea is to look for symmetry when choosing the designs. One option is clearly "at random", but I wanted to have some more structure than that. This led to the question as to how to allocate the designs. Then I started to reach the end of the stack of paper and could no longer pick a single design for a model but had to use more than one design. When I first got it, I happily made icosahedra and dodecahedra and other-ahedra with a single design of paper for each. Mind you, my introduction to it was the interlocking tetrahedra which isn't the easiest of models to make!Ī few years ago, I came across a book called Zen Origami which has lots of very nice modules to make and which comes with its own set of lovely paper. You can start with something quite simple, practise it a lot, and still end up with quite a nice single model at the end (rather than 50 paper boxes). I think that modular origami is my favourite type of origami.
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