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  2. 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]

  3. Symmetry - Wikipedia

    en.wikipedia.org/wiki/Symmetry

    Many animals are approximately mirror-symmetric, though internal organs are often arranged asymmetrically. In biology, the notion of symmetry is mostly used explicitly to describe body shapes. Bilateral animals, including humans, are more or less symmetric with respect to the sagittal plane which divides the body into left and right halves. [21]

  4. Shape and form (visual arts) - Wikipedia

    en.wikipedia.org/wiki/Shape_and_form_(visual_arts)

    A form is an artist's way of using elements of art, principles of design, and media. Form, as an element of art, is three-dimensional and encloses space. Like a shape, a form has length and width, but it also has depth. Forms are either geometric or free-form, and can be symmetrical or asymmetrical.

  5. Tetrahedral symmetry - Wikipedia

    en.wikipedia.org/wiki/Tetrahedral_symmetry

    T d and O are isomorphic as abstract groups: they both correspond to S 4, the symmetric group on 4 objects. T d is the union of T and the set obtained by combining each element of O \ T with inversion. See also the isometries of the regular tetrahedron. The conjugacy classes of T d are: identity; 8 × rotation by 120° (C 3)

  6. Affine symmetric group - Wikipedia

    en.wikipedia.org/wiki/Affine_symmetric_group

    The regular triangular tiling of the plane, whose symmetries are described by the affine symmetric group S̃ 3. The affine symmetric groups are a family of mathematical structures that describe the symmetries of the number line and the regular triangular tiling of the plane, as well as related higher-dimensional objects.

  7. Reflection symmetry - Wikipedia

    en.wikipedia.org/wiki/Reflection_symmetry

    The symmetric function of a two-dimensional figure is a line such that, for each perpendicular constructed, if the perpendicular intersects the figure at a distance 'd' from the axis along the perpendicular, then there exists another intersection of the shape and the perpendicular at the same distance 'd' from the axis, in the opposite ...

  8. Asymmetry - Wikipedia

    en.wikipedia.org/wiki/Asymmetry

    Asymmetry is the absence of, or a violation of, symmetry (the property of an object being invariant to a transformation, such as reflection). [1] Symmetry is an important property of both physical and abstract systems and it may be displayed in precise terms or in more aesthetic terms. [2]

  9. Symmetry in mathematics - Wikipedia

    en.wikipedia.org/wiki/Symmetry_in_mathematics

    The root system of the exceptional Lie group E 8.Lie groups have many symmetries. Symmetry occurs not only in geometry, but also in other branches of mathematics.Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations.

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