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Positive 3D gadgets extrude a top and two adjacent side faces of a frustum from a flat piece of paper using two pleats. Then a natural problem comes up whether it is possible to construct from any positive 3D gadget its ‘negative’ with the opposite unevenness by modifying the crease pattern without changing the pleats. In this paper we give an affirmative solution to this problem. For this purpose, we give a canonical construction of negative 3D gadgets with a supporting triangle on the back side, which have a natural correspondence to special flat-back positive ones among infinitely many compatible ones.

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Triangle-Supported Negative 3D Gadgets in Origami Extrusions with a Canonical Correspondence to Flat-Back Positive 3D Gadgets

  • 会议论文

  • 发表日期：

    2026年

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  • Mamoru Doi

摘要

Positive 3D gadgets extrude a top and two adjacent side faces of a frustum from a flat piece of paper using two pleats. Then a natural problem comes up whether it is possible to construct from any positive 3D gadget its ‘negative’ with the opposite unevenness by modifying the crease pattern without changing the pleats. In this paper we give an affirmative solution to this problem. For this purpose, we give a canonical construction of negative 3D gadgets with a supporting triangle on the back side, which have a natural correspondence to special flat-back positive ones among infinitely many compatible ones.