![]() If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet. This applet requires Sun's Java VM 2 which your browser may perceive as a popup. For example, a less regular tessellation is obtained when the rhombi are free to become parallelograms. It is possible to further relax the original constraints. Penrose tilings, which use two different quadrilaterals, are the best known example of tiles that forcibly create non-periodic patterns. ![]() There is an infinite number of such tessellations. As a result, it is easily morphs into a derivative of a 4, 4, 4, 4 tessellation. Non-regular tessellations are those in which there is no restriction on the order of the polygons around vertices. The one below lets loose the equilateral triangles. Accordingly, there are two implementations. The less common triangle systems are easily identified because three or six motifs will meet at a point, and the entire tessellation will have order 3 or order 6 rotation symmetry. We may only preserve either the squares or the equilateral triangles, but not both. There are two ways to set this tessellation on hinges. In particular this is what makes it semi-regular: a semi-regular tessellation combines more than one kind of regular polygons, but the same arrangement at every vertex. The tessellation itself is identified as (4, 3, 3, 4, 3) because 5 regular polygons meet at every vertex: a square, followed by two equilateral triangles, followed by a square and then again by an equilateral triangle. The applet implements a hinged realization of one semi-regular plane tessellations.
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