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- Cyclic_symmetry_in_three_dimensions abstract "This article deals with the four infinite series of point groups in three dimensions (n≥1) with n-fold rotational or reflectional symmetry about one axis (by an angle of 360°/n) does not change the object.They are the finite symmetry groups on a cone. For n = ∞ they correspond to four frieze groups. Schönflies notation is used. The terms horizontal (h) and vertical (v) imply the existence and direction of reflections with respect to a vertical axis of symmetry. Also shown are Coxeter notation in brackets, and, in parentheses, orbifold notation.Chiral:Cn, [n]+, (nn) of order n - n-fold rotational symmetry (abstract group Cn); for n=1: no symmetry (trivial group)Achiral:Cnh, [n+,2], (n*) of order 2n - prismatic symmetry (abstract group Cn × C2); for n=1 this is denoted by Cs (1*) and called reflection symmetry, also bilateral symmetry. It has reflection symmetry with respect to a plane perpendicular to the n-fold rotation axis.Cnv, [n], (*nn) of order 2n - pyramidal symmetry (abstract group Dn); in biology C2v is called biradial symmetry. For n=1 we have again Cs (1*). It has vertical mirror planes. This is the symmetry group for a regular n-sided pyramid.S2n, [2+,2n+], (n×) of order 2n (not to be confused with symmetric groups, for which the same notation is used; abstract group C2n); for n=1 we have S2 (1×), also denoted by Ci; this is inversion symmetry. It has a 2n-fold rotoreflection axis, also called 2n-fold improper rotation axis, i.e., the symmetry group contains a combination of a reflection in the horizontal plane and a rotation by an angle 180°/n. Thus, like Dnd, it contains a number of improper rotations without containing the corresponding rotations.C2h (2*) and C2v (*22) of order 4 are two of the three 3D symmetry group types with the Klein four-group as abstract group. C2v applies e.g. for a rectangular tile with its top side different from its bottom side.".
- Cyclic_symmetry_in_three_dimensions thumbnail Order_4_dihedral_symmetry_subgroup_tree.png?width=300.
- Cyclic_symmetry_in_three_dimensions wikiPageExternalLink productCd-0471010030.html.
- Cyclic_symmetry_in_three_dimensions wikiPageID "2926084".
- Cyclic_symmetry_in_three_dimensions wikiPageRevisionID "602919260".
- Cyclic_symmetry_in_three_dimensions subject Category:Symmetry.
- Cyclic_symmetry_in_three_dimensions comment "This article deals with the four infinite series of point groups in three dimensions (n≥1) with n-fold rotational or reflectional symmetry about one axis (by an angle of 360°/n) does not change the object.They are the finite symmetry groups on a cone. For n = ∞ they correspond to four frieze groups. Schönflies notation is used. The terms horizontal (h) and vertical (v) imply the existence and direction of reflections with respect to a vertical axis of symmetry.".
- Cyclic_symmetry_in_three_dimensions label "Cyclic symmetry in three dimensions".
- Cyclic_symmetry_in_three_dimensions sameAs m.08d2pq.
- Cyclic_symmetry_in_three_dimensions sameAs Q5198233.
- Cyclic_symmetry_in_three_dimensions sameAs Q5198233.
- Cyclic_symmetry_in_three_dimensions wasDerivedFrom Cyclic_symmetry_in_three_dimensions?oldid=602919260.
- Cyclic_symmetry_in_three_dimensions depiction Order_4_dihedral_symmetry_subgroup_tree.png.
- Cyclic_symmetry_in_three_dimensions isPrimaryTopicOf Cyclic_symmetry_in_three_dimensions.