Abstract
After the sensational discovery of the icosahedral quasicrystals, two dimensional quasicrystals with 8,10 and 12 fold rotational symmetries have also been found in various rapidly solidified alloys and experimental evidence will be presented here. Since these rotational symmetries are not compatible with the Bravais space lattices, they were called "noncrystallographic" point group symmetry in the past. However, it is argued that the long-range periodic translation order is only one of the results of the propagation of short-range orientation order and that the Bravais space lattice might not be a prerequisite of a crystal. During rapid solidification short-range orientation order predominates and therefore quasicrystals might occur with rotational symmetries not hitherto encountered.
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