Crease patterns: Diagonal shift variants

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:

Diagonal shift variant

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:

Double diagonal shift variant

Double diagonal shift variant

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:

Double diagonal shift variant 2

Double diagonal shift variant 2

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.

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