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  2. Rotational symmetry - Wikipedia

    en.wikipedia.org/wiki/Rotational_symmetry

    Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation.

  3. Point groups in three dimensions - Wikipedia

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

    Those with reflection in the planes through the axis, with or without reflection in the plane through the origin perpendicular to the axis, are the symmetry groups for the two types of cylindrical symmetry. Any 3D shape (subset of R 3) having infinite rotational symmetry must also have mirror symmetry for every plane through the axis. Physical ...

  4. Category:Rotational symmetry - Wikipedia

    en.wikipedia.org/wiki/Category:Rotational_symmetry

    Category: Rotational symmetry. ... Download as PDF; Printable version; In other projects ... 3D rotation group; 6-j symbol; 9-j symbol; A. Ambigram;

  5. 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.

  6. 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]

  7. Symmetry group - Wikipedia

    en.wikipedia.org/wiki/Symmetry_group

    For example: two 3D figures have mirror symmetry, but with respect to different mirror planes. two 3D figures have 3-fold rotational symmetry, but with respect to different axes. two 2D patterns have translational symmetry, each in one direction; the two translation vectors have the same length but a different direction.

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