English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

An origami extrusion is a folding of a 3D object in the middle of a flatpiece of paper, using 3D gadgets which create faces with solid angles. In thispaper we focus on 3D gadgets which create a top face parallel to the ambientpaper and two side faces sharing a ridge, with two outgoing simple pleats,where a simple pleat is a pair of a mountain fold and a valley fold. There aretwo such types of 3D gadgets. One is the conventional type of 3D gadgets with atriangular pyramid supporting the two side faces from inside. The other is thenewer type of 3D gadgets presented in our previous paper, which improve theconventional ones in several respects: They have flat back sides above theambient paper and no gap between the side faces; they are less interfering withadjacent gadgets so that we can make the extrusion higher at one time; they aredownward compatible with conventional ones if constructible; they have amodified flat-back gadget used for repetition which does not interfere withadjacent gadgets; the angles of their outgoing pleats can be changed undercertain conditions. However, there are cases where we can apply theconventional gadgets while we cannot our previous ones. The purpose of thispaper is to improve our previous 3D gadgets to be completely downwardcompatible with the conventional ones, in the sense that any conventionalgadget can be replaced by our improved one with the same outgoing pleats, butthe converse is not always possible. To be more precise, we prove that for anygiven conventional 3D gadget there are an infinite number of improved 3Dgadgets which are compatible with it, and the conventional 3D gadget can bereplaced with any of these 3D gadgets without affecting any other conventional3D gadget. Also, we see that our improved 3D gadget keep all of the aboveadvantages over the conventional ones.

Improved flat-back 3D gadgets in origami extrusions completely downward compatible with the conventional pyramid-supported 3D gadgets