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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. 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

  4. Symmetry - Wikipedia

    en.wikipedia.org/wiki/Symmetry

    The type of symmetry is determined by the way the pieces are organized, or by the type of transformation: 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]

  5. List of planar symmetry groups - Wikipedia

    en.wikipedia.org/wiki/List_of_planar_symmetry_groups

    The 17 wallpaper groups, with finite fundamental domains, are given by International notation, orbifold notation, and Coxeter notation, classified by the 5 Bravais lattices in the plane: square, oblique (parallelogrammatic), hexagonal (equilateral triangular), rectangular (centered rhombic), and rhombic (centered rectangular).

  6. 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.

  7. Point groups in four dimensions - Wikipedia

    en.wikipedia.org/wiki/Point_groups_in_four...

    Point groups in this article are given in Coxeter notation, which are based on Coxeter groups, with markups for extended groups and subgroups. [6] Coxeter notation has a direct correspondence the Coxeter diagram like [3,3,3], [4,3,3], [3 1,1,1], [3,4,3], [5,3,3], and [p,2,q].

  8. Symmetry (geometry) - Wikipedia

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

    A circle is thus said to be symmetric under rotation or to have rotational symmetry. If the isometry is the reflection of a plane figure about a line, then the figure is said to have reflectional symmetry or line symmetry; [3] it is also possible for a figure/object to have more than one line of symmetry. [4]

  9. Tetrahedral symmetry - Wikipedia

    en.wikipedia.org/wiki/Tetrahedral_symmetry

    T h, 3*2, [4,3 +] or m 3, of order 24 – pyritohedral symmetry. [1] This group has the same rotation axes as T, with mirror planes through two of the orthogonal directions. The 3-fold axes are now S 6 ( 3 ) axes, and there is a central inversion symmetry.

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