Customer Reviews

A Plethora of Polyhedra in Origami

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Fans of John Montroll's other books will know that he tends to follow a fixed set of ideas. These are that the paper should be square and that only one sheet should be used. Outside of a few basic shapes (cubes and pyramids mostly), the use of a single sheet in creating polyhedra is not very widespread. Montroll uses this book to show up that it needs not be the case.

Montroll shows how a single sheet of paper can be folded into more complex polyhedra including skeletal forms.

These models all follow a basic pattern of precreasing the paper to isolate the polyhedron's sides, and then collapsing the paper into the 3D model. Very interesting techniques, and Montroll seems to get the largest possible solid from the paper, but the single-sheet design does lose something in solidity. Many multi-piece models are very strong, but that is not the case here. However, if you like geometrics but could not bring yourself to fold 30 to 180 pieces of paper for a single model, you will love this book.

For a long time the folding of polyhedras and other variations is dominated by modular origami, a category of paperfolding that models are assembled by many units of the same form. Such technic has been developed into a wildly splended state, for example, see books of Lewis Simon or Tokomo Fuse. However, in this book Montroll still insists on his long-time philosophy-- one single square paper, two hands, nothing else.

The best part of this book, in my opinion, is the 5 Plato polyhedras plus the 5 sunken Plato polyhedras, all folded by a single square paper. This is a succint approach, although not new. And the intrinsic beauty of these models explains everything. Other parts of this book are fair enough, for example, prisms and other models are relatively new compared to other polyhedra origami books.

Since every model is folded by one square, it seems that we can not hope to have some super-complex models. After all, the special symmetry structures of polyhedras do hinder the design of the folding-- in order to keep symmetry it will waste too much paper. So it is a pity for those super-hard-model-addicts.

BTW, I am happy that after so many years Montroll finally comes to Mathematics!

Although folding polyhedra is not my favourite, nevertheless I do indulge in it.

Most of the polyhedra are folded as modulars. John Montroll folds them using a single square. Quite a challenge since most of the models are not simple to fold.

Models in this book include tetrahedron, cube, octahedron, icosahedron, decahedron, double diamond hexhedron, triangular dipyramid, pentagonal dipyramid, hexagonal dipyramid, heptagonal dipyramid, triangular prism, pentagonal prism, hexagonal prism, sunken platonic solids and many others.

I prefer folding polyhedra using modular techniques since they end up much more colourful. In this book polyhedra are folded using a square and hence only in one colour.

At the end of the book, Montroll gives suggestions on how to expand on the techniques he uses in this book to create your own one piece polyhedra.

Yes, I recommend this book for polyhedra enthusiast.

I really liked this book because it explains how to do all of the complicated folds. It also shows you a picture for each step so you can see what to do. I do not think that beginners should start with this book because some of the folding steps are a little hard to follow.

This origami book is interesting, and it contains many unique ideas. The models can be very elegant if folded well. That being said, it is almost impossible to fold them well, as most of them are extremely difficult to fold accurately. A _lot_ of patience is needed, much more so than modular origami, to really use and appreciate this book.