Some articles on rotocenters:
Hexagonal Lattice
... A pattern with 3- or 6-fold rotational symmetry has a lattice of 3-fold rotocenters (including possible 6-fold rotocenters) that is this finer lattice relative to the lattice of translational ... applies p3m1 with reflection axes along the shortest connections between the rotocenters p31m in the main translation directions In the 6-fold case ... there are reflection axes in the main translation directions, one of the three sets of rotocenters play a different role than the other two these reflection axes pass through them ...
... A pattern with 3- or 6-fold rotational symmetry has a lattice of 3-fold rotocenters (including possible 6-fold rotocenters) that is this finer lattice relative to the lattice of translational ... applies p3m1 with reflection axes along the shortest connections between the rotocenters p31m in the main translation directions In the 6-fold case ... there are reflection axes in the main translation directions, one of the three sets of rotocenters play a different role than the other two these reflection axes pass through them ...
Formal Treatment - Rotational Symmetry With Translational Symmetry
... There are two rotocenters per primitive cell. 2-fold rotocenters (including possible 4-fold and 6-fold), if present at all, form the translate of a lattice equal to the translational lattice, scaled by a factor 1/2. 3-fold rotocenters (including possible 6-fold), if present at all, form a regular hexagonal lattice equal to the translational lattice, rotated by 30 ...
... There are two rotocenters per primitive cell. 2-fold rotocenters (including possible 4-fold and 6-fold), if present at all, form the translate of a lattice equal to the translational lattice, scaled by a factor 1/2. 3-fold rotocenters (including possible 6-fold), if present at all, form a regular hexagonal lattice equal to the translational lattice, rotated by 30 ...
Square Lattice - Symmetry
... A pattern with 4-fold rotational symmetry has a square lattice of 4-fold rotocenters that is a factor √2 finer and diagonally oriented relative to the ... square grid which is as fine as, and oriented the same as, the square lattice of 4-fold rotocenters, with these rotocenters at the centers of the squares formed by the reflection axes ... the arrangement within a primitive cell of the 2- and 4-fold rotocenters (also applicable for p4g and p4m) ...
... A pattern with 4-fold rotational symmetry has a square lattice of 4-fold rotocenters that is a factor √2 finer and diagonally oriented relative to the ... square grid which is as fine as, and oriented the same as, the square lattice of 4-fold rotocenters, with these rotocenters at the centers of the squares formed by the reflection axes ... the arrangement within a primitive cell of the 2- and 4-fold rotocenters (also applicable for p4g and p4m) ...
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