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 A fractal tiling of both octahedral and icosahedral symmetry
 A variant of the Apollonian gasket with icosahedral symmetry
 Apollonian gasket as a fractal in tiled hyperbolic space
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Monthly Archives: July 2012
Another tiling of dodecagonal symmetry
We consider selfsimilarities and iteration methods for quasiperiodic tilings of 12fold symmetry. In “Iteration of rhombs: filling the gap (2)” the ratio of the lengths at each iteration step is sqrt(2+sqrt(3))=sqrt(3.73)=1.91. The Stampfli tiling has a selfsimilarity (see “Exhibition of … Continue reading
Posted in Tilings
Tagged Geometry, Iterative method, quasiperiodic Tiling, Selfsimilarity
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Another tiling with octagons
I am addicted to iterative methods. They are easy to program and yield surprising results. I like to work out new iterative schemes, which have often their particular beauty. But the great suspense arises when running them first time on … Continue reading
Posted in Tilings
Tagged Ammannâ€“Beenker tiling, Iterative method, quasiperiodic Tiling, Rotational symmetry
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A special threecolor symmetry
Earlier I have presented a coloring of the AmmanBeenker tiling which exchanges colors upon translation, see “Twofold color symmetry in translation” and “Twofold color symmetry in translation – revisited“. It resulted from the square checkerboard. As there are many similarities … Continue reading
Posted in Tilings
Tagged Color, quasiperiodic Tiling, Selfsimilarity, translational symmetry
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Threecolor symmetry in rotation for the Stampfli tiling
I am going back to color symmetries of the Stampfli tiling. In an earlier post I showed a twocolor symmetry in rotation. Now I am discussing a symmetry with three colors. A rotation of the tiling by 30 degrees should … Continue reading
Variations on a star
I still have a lot to do on tilings of 12fold rotational symmetry – but summer is too hot to do serious work. Meanwhile I amuse myself with iterative decorations. Two triangles superimposed form a sixpointed star. This is a … Continue reading
Posted in Anamorphosis, Extra
Tagged inversive geometry, Iterative method, Rotational symmetry
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Another enantiomorphic tiling
In the last post “doubling the tessellation of squares and triangles” I have shown a quasiperiodic tiling with an unusual mirror symmetry. Earlier in “Morphing the tiling … a new twist” I got a tiling which is not at all … Continue reading
Posted in Tilings
Tagged enantiomorphic, Geometry, Iterative method, mirror symmetry, quasiperiodic Tiling
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Doubling the tessellation of squares and triangles
Equilateral triangles do not fit well with fourfold rotational symmetry. Yet there exists a semiregular tessellation having both. It has unusual symmetries. The centers of the rotational symmetries are at the center of the squares. It is mirror symmetric but … Continue reading
Posted in Tilings
Tagged enantiomorphic, Geometry, mirror symmetry, quasiperiodic Tiling, Rotational symmetry
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