![]() I also found some four-color patterns with interesting symmetry:įinally, here are some which each use six colors. ![]() Here are some which use three colors each: As another example of ongoing work in finding interesting recreational uses of tilings and patterns, Erik and Martin Demaine, working with Scott Kim and Yushi Uno, released a tiling font in 2021, where each character can be used to tile the plane Citation 2. Next, with construction artifacts hidden, are some two-color designs I found. At some point (which I expect would vary from person to person), as the order-number increases, the hexagons needed will become so thin that they will no longer be recognizable as hexagons. There are 14 demiregular (or polymorph) tessellations which are orderly compositions of the three regular and eight semiregular tessellations (Critchlow 1970, pp. 6, tells us there are 3 vertices with 2 different vertex types. 1 This notation represents (i) the number of vertices, (ii) the number of polygons around each vertex (arranged clockwise) and (iii) the number of sides to each of those polygons. No upper limit exists to the order-number of these all-hexagon radial tessellations - although the larger that number gets, the thinner the hexagons become, relative to their edge length. Euclidean tilings are usually named after Cundy & Rollett’s notation. In the first picture, the construction-circles, -points, and -lines I used are shown in the rest, they are hidden. As it turns out, this particular radial tessellation lends itself particularly well to a variety of coloring-schemes. This left out order-6, of which I show many examples below. The idea is that the design could be continued infinitely far to cover the whole plane (though of course we can only draw a small portion of it). In that previous post, examples were shown of order 4, 5, and 8, in addition to the familiar order-3 regular-hexagon tessellation. A tessellation is a design using one ore more geometric shapes with no overlaps and no gaps. With higher-order all-hexagon radial tessellations, though, the hexagons must be elongated, although they can still remain equilateral, and all congruent, with bilateral symmetry. Order-three tessellations of this type are the familiar regular-hexagon tessellations of the plane. Spherical tessellations Examples of spherical tessellations in the real world are not as common as planar tessellations, but they can be seen in a variety of settings. ![]() You will need the following supplies to create a tessellation by hand: a pencil or pen, a 3 by 5 index card, scissors, tape, an 8. (10 points) Part 3: Create a tessellation by hand. These are shown in Figure 3.20, along with examples of tessellations requiring three and four colors. Create an irregular tessellation using the grid below by modifying one of the squares, performing a glide reflection, and continuing the pattern to fill the grid. I explored radial tessellations of the plane, using only hexagons, in this earlier post. Only two of the eight semi-regular tessellations can be two colored. ![]()
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