#Tessellation examples software#

Most origami enthusiasts construct a basic pattern by marking a square or equilateral triangle grid on one sheet of paper and placing twist folds along the grid. If each of the two basic patterns has a square- or triangle-shaped boundary, as well as rotational and mirror symmetries, then we construct an origami tessellation by connecting the two patterns (Fig. For example, two basic patterns with mirror symmetry at the connecting edge hold this condition. To connect two basic patterns, the edges to be connected must be folded in the same way. (d) A pattern constructed by two (b) and two mirror symmetry (b).Ī crease pattern of an origami tessellation is composed of basic patterns. (c) A pattern constructed by three (a) and three mirror symmetry (a). Many of the basic patterns are single twist fold or multiple twist folds connected.Įxamples of basic patterns and twist folds. Figure 2a and b is also called twist folds folded while twisting the center of the paper.

Figure 2 shows examples of basic patterns. It is a basic module of an origami tessellation.

In this paper, we call such a pattern a basic pattern. Like this example, many origami tessellations have a periodic arrangement of patterns that can be folded into a smaller similar shape. When the hexagon pattern is folded, each boundary edge has two Z-shape overlaps, and the boundary becomes a small hexagon. It has a periodic arrangement of hexagonal patterns in Fig. The crease pattern of the piece is shown in Fig. Valley crease lines are for sinking and folding. Mountain crease lines are for rising and folding. An origami piece can be defined by its crease pattern, which contains a set of mountain and valley crease lines (shown in red single dotted and blue dotted in this paper) appearing on a sheet of paper when the origami is opened flat. An example of an origami tessellation is shown in Fig.

Origami tessellations are geometric pieces folded from a single sheet of paper with flatly overlapped facets.

#Tessellation examples software#

As a result, a grid-independent construction method was proposed, and new origami tessellations were obtained by using software that implements the method.Ī hole problem for designing general origami is redefined by restricting it to origami tessellations.Ī method for constructing a crease pattern of connected triangle twist folds is presented.Ī method for constructing origami tessellations without using a grid is proposed.Ī set of triangle twist folds that constitute some existing origami tessellation is revealed. 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. 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. This paper proposes a new construction method for origami tessellations that solves this problem and enriches these varieties. 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. 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.