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Collapsing the base is often the most tricky part of doing a CP. Draw the crease lines on the CP; it'll make it easier for you to know where to fold. Identify the direction of the creases - adjacent creases usually alternate between valley and mountain folds. However, do not be too hung up on it if it looks like the crease direction is wrong. Just start from where you're confident of the direction, and eventually the creases will pop into place correctly. Start collapsing sub-bases and then work your way from those. If a certain region becomes intractable, isolate that region on a separate sheet of paper and figure out how it collapses.
Do not assume that the CP should collapse into a flat base. Some models, particularly those with a closed back structure, rely on a three dimensional basic structure. Study all the available photos of the model. Try and subtract the final details on the model and imagine what the basic structure should look like, and try to achieve that.
Don't assume that the CP is correct either. Just like any other stuff on the net, CPs are mostly unverified since designers don't often get much feedback on those. Unfortunately, an error in a CP is often much much worse than an error in a diagram.
Many symmetric (and some not so symmetric) crease patterns are still built upon two bases: the Bird base and the Frog base. Both of these bases ultimately arise from a preliminary base (or equivalently, the waterbomb base). We can use this fact to help us collapse crease patterns into flat bases, assuming they exist.
If we take a close look at some of the crease patterns listed in the next two sections, we see that many of them have a point around the centre of the square, from which many long creases radiate (often, these are the uniaxial creases, if the base is uniaxial to begin with). This is the central point of the base upon which the model is folded. By starting a preliminary or waterbomb base around this central point, we can eventually reach the collapsed base by a combination of squash, petal and swivel folds.
A straightforward example of this "central starting point" method would be any model with a diagonal squares arrangement. A preliminary base is first formed at the common apex of both squares, and then the creases in the four sections filled in and collapsed to form the final base.
For models like Mark Leonard's Wolf or Noburu Miyajima's horse, a preliminary base can be similarly formed. Each of the four sides of the base are then squash folded - the final base can then be obtained by filling in the creases around this squash-folded preliminary base.
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