Abstract

Origami tessellations are geometric pieces folded from a single sheet of paper with flatly overlapped facets. Most existing origami tessellations are constructed by first marking a grid of crease lines on the paper and then arranging repeating patterns along the grid. However, this design method is limited because it cannot design origami tessellations with patterns that cannot be represented on a grid, such as a regular pentagon. This paper proposes a new construction method for origami tessellations that solves this problem and enriches these varieties. In the proposed method, a boundary of an origami tessellation is determined first, and then patterns called triangle twist fold patterns are placed inside the boundary. A similar approach is known as a hole problem, although in this paper, the problem is redefined and discussed in a form suitable for origami tessellations. As a result, a grid-independent construction method was proposed, and new origami tessellations were obtained by using software that implements the method.

中文翻译：

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用三角形扭曲折叠解决折纸镶嵌孔问题的方法

摘要

折纸镶嵌是由单张纸折叠而成的几何碎片，具有平坦重叠的刻面。大多数现有的折纸镶嵌是通过首先在纸上标记折线网格然后沿着网格排列重复图案来构建的。但是，这种设计方法受到限制，因为它无法设计具有无法在网格上表示的图案的折纸镶嵌，例如正五边形。本文提出了一种新的折纸镶嵌方法，解决了这个问题，丰富了这些品种。在所提出的方法中，首先确定折纸镶嵌的边界，然后将称为三角形扭曲折叠图案的图案放置在边界内。类似的方法被称为孔问题，尽管在本文中，该问题以适合折纸镶嵌的形式重新定义和讨论。因此，提出了一种与网格无关的构造方法，并通过使用实现该方法的软件获得了新的折纸镶嵌。