I discovered incire a few years back at a craft show. It’s a method of cutting paper so that when some cut elements are folded, they can be tucked to the element next to it, making a lacy effect. Sometimes this is also called “lace” and not incire, which makes it difficult searching for it online. There does seem to be metal dies and probably cutting patterns for this craft, but I have not seen many finished examples of it online. On the old site, the user from this blog https://www.extremepapercrafting.com/search?q=+incire posted her Christmas Tree pattern (sorry, I’ve forgotten her username there), and I’ve found one or two sites with finished examples. But otherwise, sites just sell patterns and there seems to be an out-of-print book by Nellie Snellen.
I hand cut a very basic incire pattern (just diagonal slits) to make these greeting card hands (or you can imagine them as gloves with stitching). It’s nice to use paper with a contrasting color beneath so the effect stands out when the incire is tucked and folded.
I also used a piece of the same incire pattern on these cards, just a larger piece of it with a contrasting color glued on the back.
And here is another card style using cardstock with a different color on both sides, but basically using the same diagonal cutting.
For these last few I found patterns online that I traced by hand and cut. It was more difficult cutting these by hand, even with small scissors.