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2. List of spherical symmetry groups - Wikipedia

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

   There are five fundamental symmetry classes which have triangular fundamental domains: dihedral, cyclic, tetrahedral, octahedral, and icosahedral symmetry. This article lists the groups by Schoenflies notation , Coxeter notation , [ 1 ] orbifold notation , [ 2 ] and order.

3. Point groups in three dimensions - Wikipedia

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

   C i (equivalent to S 2) – inversion symmetry; C 2 – 2-fold rotational symmetry; C s (equivalent to C 1h and C 1v) – reflection symmetry, also called bilateral symmetry. Patterns on a cylindrical band illustrating the case n = 6 for each of the 7 infinite families of point groups. The symmetry group of each pattern is the indicated group.

4. Symmetry in mathematics - Wikipedia

   en.wikipedia.org/wiki/Symmetry_in_mathematics

   Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. [ 1 ] Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure.

5. Symmetry (geometry) - Wikipedia

   en.wikipedia.org/wiki/Symmetry_(geometry)

   A drawing of a butterfly with bilateral symmetry, with left and right sides as mirror images of each other.. In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under the transform). [1]

6. Cyclic symmetry in three dimensions - Wikipedia

   en.wikipedia.org/wiki/Cyclic_symmetry_in_three...

   It has reflection symmetry with respect to a plane perpendicular to the n-fold rotation axis. C nv, [n], (*nn) of order 2n - pyramidal symmetry or full acro-n-gonal group (abstract group Dih n); in biology C 2v is called biradial symmetry. For n=1 we have again C s (1*). It has vertical mirror planes. This is the symmetry group for a regular n ...

7. List of planar symmetry groups - Wikipedia

   en.wikipedia.org/wiki/List_of_planar_symmetry_groups

   This article summarizes the classes of discrete symmetry groups of the Euclidean plane. The symmetry groups are named here by three naming schemes: International notation, orbifold notation, and Coxeter notation. There are three kinds of symmetry groups of the plane: 2 families of rosette groups – 2D point groups; 7 frieze groups – 2D line ...