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单词 crystallographic groups
释义

crystallographic groups

A planar crystallographic group or wallpaper group is a group of isometries of the plane which has a subgroup of translations that is isomorphic to ℤ2. (Compare frieze groups.)

A ‘herringbone' wallpaper

The symmetry group of the pattern in the figure is one such wallpaper group. It contains translations and glide reflections but has no non-trivial rotational symmetry. In all there are 17 wallpaper groups (up to isomorphism).

In three dimensions there are 230 crystallographic groups and in four dimensions there are 4783.

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更新时间:2025/6/19 10:07:03