Monthly Archives: August 2012

Doubling the tesselation of dodecagons, hexagons and squares

Today I am looking again at a semiregular tessellation with hexagonal symmetry. But this tessellation is the most complex one. I can get all tessellations of the earlier posts from the grid of this tessellation just by leaving out one … Continue reading

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The L2-tiling is not self-similar !

In my earlier post “Doubling the tessellation of hexagons and triangles” I found a tiling with a rather high density of stars of twelve rhombs. I called it the L2-tiling. To see if the L2-tiling is self-similar I let the … Continue reading

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Doubling the tessellation of hexagons, squares and triangles

There is a nice semiregular tessellation with sixfold rotational symmetry made of hexagons, squares and triangles. Its grid is easy to find. From two of these grids we get a rather complicated tiling with twelvefold rotational symmetry: Note that we … Continue reading

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Doubling the tesselation of dodecagons and triangles

It is still too hot for my brain to do something really new and thus I continue with the semiregular tessellations. Today I am looking at the tessellation of dodecagons and triangles. Dodecagons are regular polygons with twelve sides. The … Continue reading

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Doubling the tessellation of hexagons and triangles

With the dualization method we can use all semiregular tessellations of six-fold symmetry to make quasiperiodic tilings of 12-fold symmetry. We begin with the tessellation of hexagons and triangles. It has many intertwined stars. Its generating grid consists of rhombs. … Continue reading

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Doubling the tesselation of hexagons

We continue with the dualization method. Here again I am not presenting something really new. I am just trying to put things together. It was probably Socolar who first used the dualization method to get a quasiperiodic tiling of 12-fold … Continue reading

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Doubling the tesselation of triangles

Using the dualization method we get a the regular tiling of equilateral triangles from a grid of regular hexagons. Each point of the grid where three lines makes a triangle. Its sides are perpendicular to the grid lines. To get … Continue reading

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