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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
Posted in Tilings
Tagged dual tesselation, quasiperiodic Tiling, Rotational symmetry
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The L2tiling is not selfsimilar !
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 L2tiling. To see if the L2tiling is selfsimilar I let the … Continue reading
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
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
Posted in Tilings
Tagged dual tesselation, quasiperiodic Tiling, Rotational symmetry, shield tiling, Socolar tiling
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Doubling the tessellation of hexagons and triangles
With the dualization method we can use all semiregular tessellations of sixfold symmetry to make quasiperiodic tilings of 12fold symmetry. We begin with the tessellation of hexagons and triangles. It has many intertwined stars. Its generating grid consists of rhombs. … Continue reading
Posted in Tilings
Tagged dual tesselation, quasiperiodic Tiling, Rotational symmetry, Selfsimilarity
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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 12fold … Continue reading
Posted in Tilings
Tagged dual tesselation, quasiperiodic Tiling, Selfsimilarity, shield tiling, Socolar tiling, Stampfli tiling
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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
Posted in Tilings
Tagged dual tesselation, quasiperiodic Tiling, Selfsimilarity, Stampfli tiling
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Quasiperiodic tiling with pentagons – the Penrose connection
The last post “A quasiperiodic tiling with pentagons” is close to the original reasoning of Penrose, see the article “Penrose tiling” in Wikipedia. He dissected the Pentagon into six smaller ones and filled the gaps with other tiles. He took … Continue reading
Posted in Tilings
Tagged fractal, Iterative method, Penrose tiling, pentagon, pentagram, quasiperiodic Tiling
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A quasiperiodic tiling with pentagrams
I wanted to eliminate the gaps appearing in the earlier post “Iteration of pentagrams“. The pentagon that surrounds the pentagram should ultimately be filled up with pentagrams of different sizes. The six pentagrams of the earlier iteration scheme are shown … Continue reading
Posted in Tilings
Tagged iteration, Iterative method, Penrose tiling, pentagram, quasiperiodic Tiling
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Iteration of pentagrams
This one is rather complicated as I could also call it “Iteration of Pentagons”. The figure shows the primary pentagram as a violet shade. The thin lines give its surrounding pentagon. We can dissect the pentagram into a small central … Continue reading
Posted in Tilings
Tagged fractal design, Iterative method, Penrose tiling, pentagon, pentagram, Rotational symmetry, Selfsimilarity
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