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Over the past several years I've been playing with a certain member of the Zig-Zag family of modular origami units. Zig-Zag units are modular origami folds whose locking mechanism is based on an accordion pleat. That is, you accordion pleat a square, typically into 4ths or 3rds, making a rectangle. The short ends of the rectangle become the flaps, and the layers at the sides created by the accordion folds become the pockets. Of course, other folds in the rectangle are needed to make the flaps hook and stay, but that's the basic concept. Lots of modular origami units exist that fall into this category, units by creators such as Robert Neale, Lewis Simon, Jeannine Mosely, and Jun Maekawa, just to name a few.

The unit I've been using extensively is what I call the pentagon-hexagon zig-zag unit (or PHiZZ unit). I call it this because you can use it to make any polyhedron that is cubic - each corner of the polyhedron has three edges meeting it, and has only pentagon and hexagon faces (the faces need not be regular).

(Of course, you can break these rules in various ways, say, by making square faces. But the units tend to buckle when forced to do this. Or you could make the vertices have degree 4 (I know of two ways you can do this), and that's interesting too. But for this exposition I'll just stick to the above rules.)

The unit itself is very simple, and the first thing I made with it was a dodecahedron. But then I noticed that the locking mechanism in this unit is particularly strong, allowing one to make much larger structures. Thus began my quest to see exactly what other polyhedra you could make with this unit and, later on, how to properly 3-color them.

Thomas Hull

Источник: http://kahuna.merrimack.edu

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PHiZZ додекаэдр
PHiZZ додекаэдр
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Phizz 90
Phizz 90
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Цветочный шарик
Цветочный шарик
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PHIZZ
PHIZZ
pentagon-hexagon zig-zag unit
пяти-шести угольный модуль
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