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  2. Schoenflies notation - Wikipedia

    en.wikipedia.org/wiki/Schoenflies_notation

    The Schoenflies (or Schönflies) notation, named after the German mathematician Arthur Moritz Schoenflies, is a notation primarily used to specify point groups in three dimensions. Because a point group alone is completely adequate to describe the symmetry of a molecule , the notation is often sufficient and commonly used for spectroscopy .

  3. Crystallographic point group - Wikipedia

    en.wikipedia.org/wiki/Crystallographic_point_group

    In Schoenflies notation, point groups are denoted by a letter symbol with a subscript. The symbols used in crystallography mean the following: C n (for cyclic) indicates that the group has an n-fold rotation axis.

  4. List of space groups - Wikipedia

    en.wikipedia.org/wiki/List_of_space_groups

    In Schoenflies notation, the symbol of a space group is represented by the symbol of corresponding point group with additional superscript. The superscript doesn't give any additional information about symmetry elements of the space group, but is instead related to the order in which Schoenflies derived the space groups.

  5. Point groups in three dimensions - Wikipedia

    en.wikipedia.org/wiki/Point_groups_in_three...

    Coxeter notation offers a bracketed notation equivalent to the Coxeter diagram, with markup symbols for rotational and other subsymmetry point groups. In Schoenflies notation, the reflective point groups in 3D are C nv, D nh, and the full polyhedral groups T, O, and I.

  6. List of spherical symmetry groups - Wikipedia

    en.wikipedia.org/wiki/List_of_spherical_symmetry...

    John Conway uses a variation of the Schoenflies notation, based on the groups' quaternion algebraic structure, labeled by one or two upper case letters, and whole number subscripts. The group order is defined as the subscript, unless the order is doubled for symbols with a plus or minus, "±", prefix, which implies a central inversion .

  7. Dihedral symmetry in three dimensions - Wikipedia

    en.wikipedia.org/wiki/Dihedral_symmetry_in_three...

    Schönflies notation is used, with Coxeter notation in brackets, and orbifold notation in parentheses. The term horizontal (h) is used with respect to a vertical axis of rotation. In 2D, the symmetry group D n includes reflections in lines. When the 2D plane is embedded horizontally in a 3D space, such a reflection can either be viewed as the ...

  8. List of planar symmetry groups - Wikipedia

    en.wikipedia.org/wiki/List_of_planar_symmetry_groups

    The 17 wallpaper groups, with finite fundamental domains, are given by International notation, orbifold notation, and Coxeter notation, classified by the 5 Bravais lattices in the plane: square, oblique (parallelogrammatic), hexagonal (equilateral triangular), rectangular (centered rhombic), and rhombic (centered rectangular).

  9. Oblique lattice - Wikipedia

    en.wikipedia.org/wiki/Oblique_lattice

    The oblique lattice class names, Schönflies notation, Hermann-Mauguin notation, orbifold notation, Coxeter notation, and wallpaper groups are listed in the table below. Geometric class, point group Arithmetic