![]() ![]() The key features of tessellations are that there are no gaps or overlaps. What are the main features of tessellations? A semi-regular tessellation is made of two or more regular polygons.A regular tessellation is a pattern made by repeating a regular polygon.A Tessellation (or Tiling) is when we cover a surface with a pattern of flat shapes so that there are no overlaps or gaps.Once students know what the length is of the sides of the different tiles, they could use the information to measure distances. … Tiles used in tessellations can be used for measuring distances. Since tessellations have patterns made from small sets of tiles they could be used for different counting activities. Certain shapes that are not regular can also be tessellated. Regular polygons tessellate if the interior angles can be added together to make 360°. What is tessellation and how does it work?Ī tessellation is a pattern created with identical shapes which fit together with no gaps. Although tessellations can be made from a variety of different shapes, there are basic rules that apply to all regular and semi-regular tessellation patterns. Tessellations are used in works of art, fabric patterns or to teach abstract mathematical concepts, such as symmetry. … A tiling that lacks a repeating pattern is called “non-periodic”. In mathematics, tessellations can be generalized to higher dimensions and a variety of geometries. The initial known data are essentially the shape and size of the central part of the molecule (the quadrilateral $V_1V_2V_3V_4$ in the figure),ĭefined completely by 3 of its corners and 2 of its sides, the position of the center $P_1$ within the central part, and the $E_i$ convergence point of the double pleat for each strip $i$, with $1 \leq i \leq 4$.A tessellation or tiling of a flat surface is the covering of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. With the first vertex of the central part corresponding to the center of the axes of the plane, and the base of the central part lying on the x-axis. Let's consider figure 9 in which a complete and valid crease pattern of a molecule is reported on the Cartesian plane, Let's analyze below the case of a molecule with 4 branches (4 strips). Starting from the final valid crease pattern of a molecule, we can use analytic geometry to calculate the values of the points of interest and segments of the crease pattern, based on the initial known data. 5d.ĭ) Backside of the completed node Figure 8 - Practical example of use of the geometric construction algorithm of the molecule Analytical calculation 5c).Īt this point, the remaining two rectangles that we have to add will have a compulsory width, determined by their joining point, which will be the vertex of the polygon on the top left, as shown in fig. 5b), and we add a rectangle of small width at will 3īetween the two polygons below, and a rectangle between the two polygons on the right (fig. Let's imagine opening the node mentioned (fig. Having said that, let's start from the node you want to make (i.e. ![]() When folded, allows us to join the edges of the adjacent polygons, to form the final node with flagstone effect (vedi fig. So, let's start by saying that the "strips" of paper between the polygons, constitute the excess of paper that, Now, let's first see how to determine these rectangular paper strips between the polygons, and then move on to the construction of the relative molecule. ![]() The rectangles of paper, instead, corresponding to the lines that form the node, will be called "strips" of the node. In the image below there are some examples of these tessellations.Ĭ) Crease Pattern Figure 3 - Example of "flagstone" tessellation – Highlighted tile They are reminiscent of flagstone flooring, hence the name "flagstone". These are tessellations in which the edges of the tiles forming them are adjacent and on the same level, without overlapping. One of these subgroups is that of flagstone tessellations. The origami tessellations can be divided into various subgroups, each with its own particular characteristics. Unlike geometric tessellations, the tessellations can be both flat and three-dimensional. Similarly, in the origami world, all those models formed by equal (or even similar) "tiles" that are repeated in the surface are called tessellations.Įach tessellation is always made from a single sheet of paper properly folded. In plane geometry, the term tessellation indicates the covering of the plane with one or more geometric figures (called "tiles") repeated infinitely, without overlapping and without spaces between them. ![]()
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