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  2. Symmetry (geometry) - Wikipedia

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

    Reflectional symmetry, linear symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection. [ 8 ] In one dimension, there is a point of symmetry about which reflection takes place; in two dimensions, there is an axis of symmetry (a.k.a., line of symmetry), and in three dimensions there is a ...

  3. Symmetry - Wikipedia

    en.wikipedia.org/wiki/Symmetry

    An object has reflectional symmetry (line or mirror symmetry) if there is a line (or in 3D a plane) going through it which divides it into two pieces that are mirror images of each other. [6] An object has rotational symmetry if the object can be rotated about a fixed point (or in 3D about a line) without changing the overall shape. [7]

  4. Symmetry in mathematics - Wikipedia

    en.wikipedia.org/wiki/Symmetry_in_mathematics

    A symmetry of a differential equation is a transformation that leaves the differential equation invariant. Knowledge of such symmetries may help solve the differential equation. A Line symmetry of a system of differential equations is a continuous symmetry of the system of differential

  5. Reflection symmetry - Wikipedia

    en.wikipedia.org/wiki/Reflection_symmetry

    In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2-dimensional space, there is a line/axis of symmetry, in 3-dimensional space, there is a plane of symmetry

  6. Point reflection - Wikipedia

    en.wikipedia.org/wiki/Point_reflection

    A point reflection is an involution: applying it twice is the identity transformation. An object that is invariant under a point reflection is said to possess point symmetry (also called inversion symmetry or central symmetry). A point group including a point reflection among its symmetries is called centrosymmetric.

  7. Symmetry element - Wikipedia

    en.wikipedia.org/wiki/Symmetry_element

    The elements of this symmetry group should not be confused with the "symmetry element" itself. Loosely, a symmetry element is the geometric set of fixed points of a symmetry operation. For example, for rotation about an axis, the points on the axis do not move and in a reflection the points that remain unchanged make up a plane of symmetry.

  8. Point groups in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Point_groups_in_two_dimensions

    The symmetry group of a square belongs to the family of dihedral groups, D n (abstract group type Dih n), including as many reflections as rotations. The infinite rotational symmetry of the circle implies reflection symmetry as well, but formally the circle group S 1 is distinct from Dih(S 1) because the latter explicitly includes the reflections.

  9. Symmetry operation - Wikipedia

    en.wikipedia.org/wiki/Symmetry_operation

    In mathematics, a symmetry operation is a geometric transformation of an object that leaves the object looking the same after it has been carried out. For example, a 1 ⁄ 3 turn rotation of a regular triangle about its center, a reflection of a square across its diagonal, a translation of the Euclidean plane, or a point reflection of a sphere through its center are all symmetry operations.

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