This is a glide reflection, except in the special case that the translation is perpendicular to the line of reflection, in which case the combination is itself just a reflection in a parallel line.
32.
In Euclidean geometry a transformation is a one-to-one correspondence between two sets of points or a mapping from one plane to another . ) A translation can be described as a reflections and glide reflections.
33.
Glide reflection symmetry with respect to two parallel lines with the same translation implies that there is also translational symmetry in the direction perpendicular to these lines, with a translation distance which is twice the distance between glide reflection lines.
34.
Glide reflection symmetry with respect to two parallel lines with the same translation implies that there is also translational symmetry in the direction perpendicular to these lines, with a translation distance which is twice the distance between glide reflection lines.
35.
Along with translations, rotations, reflections, as well as the identity transformation, Euclidean motions comprise also glide reflections ( for ), screw operations and rotoreflections ( for ), and even more complex combinations of primitive transformations for.
36.
The symmetry group is sometimes also called "'full symmetry group "'in order to emphasize that it includes the orientation-reversing isometries ( like reflections, glide reflections and improper rotations ) under which the figure is invariant.
37.
The axis of the mirror or glide reflection is perpendicular to the main axis for the first letter, and either parallel or tilted 180?/ " n " ( when " n " > 2 ) for the second letter.
38.
Two 2-uniform colorings have a single vertex figure, 11123, with two colors of squares, but are not 1-uniform, repeated either by reflection or glide reflection, or in general each row of squares can be shifted around independently.
39.
The same applies for a change of angle between translation vectors, provided that it does not add or remove any symmetry ( this is only the case if there are no mirrors and no glide reflections, and rotational symmetry is at most of order 2 ).
40.
A " random " isometry, like taking a sheet of paper from a table and randomly laying it back, " almost surely " is a rotation or a glide reflection ( they have three uniformly distributed and the length of the added vector has a continuous distribution.
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