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・ Line E (Buenos Aires Underground)
・ Line echo wave pattern
・ Line editor
・ Line element
・ Line Engaged
・ Line engraving
・ Line F (Buenos Aires Underground)
・ Line field
・ Line filter
・ Line fitting
・ Line Focus Principle
・ Line function
・ Line G (Buenos Aires Underground)
・ Line graph
・ Line graph of a hypergraph
Line group
・ Line H (Buenos Aires Underground)
・ Line H7 (Budapest HÉV)
・ Line Haddad
・ Line Hagman
・ Line Halvorsen
・ Line Hamel
・ Line Hansen
・ Line Henriette Holten Hjemdal
・ Line holder
・ Line honours
・ Line Horntveth
・ Line house
・ Line hunting
・ Line I (Buenos Aires Underground)


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Line group : ウィキペディア英語版
Line group
A line group is a mathematical way of describing symmetries associated with moving along a line. These symmetries include repeating along that line, making that line a one-dimensional lattice. However, line groups may have more than one dimension, and they may involve those dimensions in its isometries or symmetry transformations.
One constructs a line group by taking a point group in the full dimensions of the space, and then adding translations or offsets along the line to each of the point group's elements, in the fashion of constructing a space group. These offsets include the repeats, and a fraction of the repeat, one fraction for each element. For convenience, the fractions are scaled to the size of the repeat; they are thus within the line's unit cell segment.
== One-dimensional ==

There are 2 one-dimensional line groups. They are the infinite limits of the discrete two-dimensional point groups C''n'' and D''n'':

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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