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 Quasiperiodic design with 8fold rotational symmetry from 4dimensional space
 Rotational symmetry from space with an even number of dimensions
 Periodic design with 3fold rotational symmetry from 3dimensional space
 Inversion symmetry doubles the rotation symmetry for an odd number of dimensions
 quasiperiodic patterns of 5fold symmetry from 5 dimensional 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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