Crease Pattern

I’ve previously posted several crease patterns for my diagonal shift designs. Since posting those crease patterns, I designed a diagonal shift variant where the top and bottom halves of the paper form tubes of different widths and folded several models based on that design. Here are some crease patterns for a couple versions of diagonal shift variants. The dimensions on these don’t quite match any of the models I’ve folded, but they at least show the approach I used.

First, the single diagonal shift variant:

The bottom half of this crease pattern is identical to the crease patterns I posted before. Just above the middle, the diagonal lines only go partway past the middle of each gore, and the top section forms a narrower tube. This crease pattern gives something similar to the central part of this model.

These designs can also be combined in a couple ways. One option is to mirror the diagonal shift element vertically, giving a double diagonal shift pattern like the one in this vase:

Another other option is to also shift the top diagonal shift section over by 8 gores (half the width of the paper, excluding the overlap), which gives something like this model:

The math behind these designs is a good bit more complicated than I enjoy doing by hand, so I’ve set up spreadsheets to automatically do most of the math for me. I haven’t written about that aspect yet, but I might do that at some point when I have time.

Recently I have folded several test pieces and a finished model incorporating a diagonal shift element. Here are several crease patterns showing how that element works, along with some notes and folding hints below:

For each design, the “curves” marking the top and bottom of the diagonal shift are based on sine curves. The sine curves are offset by one gore (the top curve is shifted one gore right relative to the bottom gore). This allows all the mountain folds to cross the centers of their gores at exactly the same height. Without this offset, the crease pattern will not collapse correctly.

One of the biggest challenges in designing these forms is figuring out how far apart the two sine curves need to be. I wrote an Excel spreadsheet to automatically calculate the correct distance based on the angles and distances in the crease pattern.

Of course, this element can be incorporated into more complex models, like I did recently. I’m working on folding more models of this sort.

The seed pod bowl is one of my most popular models, and I’ve gotten more requests for its crease pattern than for any of my other models. I finally drew the crease pattern:

As with all my crease patterns, the red lines are mountain folds and the blue lines are valley folds. The top side of the paper will become the inside of the form.

A few notes:

1. The mountain/valley pattern on this model is the opposite as it is for most of my models. Viewed from the inside of the final form, the straight folds are mountains and the curved folds are valleys.
2. Since this model does not have a flat base and is not a tube, the collapse process is a bit different that my other models. Briefly, I used a combination of tape and glue to hold the creases in place at the two ends of the form, and wet-folded to create the curved form.
3. Given the crease pattern as drawn, the model will be curved all the way around and not sit flat. I fixed that problem by making a small dent where I wanted the base (not shown on the crease pattern).