If the translation vector of a glide plane operation is itself an element of the translation group, then the corresponding glide plane symmetry reduces to a combination of reflection symmetry and translational symmetry.
22.
The translational symmetry is given by oblique translation vectors from one point on a true reflection line to two points on the next, supporting a rhombus with the true reflection line as one of the diagonals.
23.
Combining two equal glide plane operations gives a pure translation with a translation vector that is twice that of the glide plane operation, so the even powers of the glide plane operation form a translation group.
24.
Performing the two operations in sequence, i . e . first the rotation and then the translation ( with translation vector given in the already rotated coordinate system ), gives a combined rotation and translation matrix
25.
The simplest representation would be to represent the map as a transformation matrix and a translation vector ( n ^ 2 + n real values ), but I'd like each value to have a single clearly defined function.
26.
The " primitive translation vectors " 1 } }, 2 } }, 3 } } span a lattice cell of smallest volume for a particular three-dimensional lattice, and are used to define a crystal translation vector
27.
The " primitive translation vectors " 1 } }, 2 } }, 3 } } span a lattice cell of smallest volume for a particular three-dimensional lattice, and are used to define a crystal translation vector
28.
As it does so, the object's motion will be described by two vectors : a translation vector, and a rotation vector "'? "', which is an areal velocity vector : the Darboux vector.
29.
In the remaining two cases symmetry description is with respect to centred cells that are larger than the primitive cell, and hence have internal repetition; the directions of their sides is different from those of the translation vectors spanning a primitive cell.
30.
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 ).
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