• Thumbnail for 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...
    8 KB (771 words) - 04:10, 28 February 2025
  • Thumbnail for Glide reflection
    transformation, it is said to have symmetry, and the transformation is called a symmetry operation. Glide-reflection symmetry is seen in frieze groups (patterns...
    13 KB (1,661 words) - 14:37, 28 May 2025
  • Thumbnail for Point reflection
    point reflection is said to possess point symmetry (also called inversion symmetry or central symmetry). A point group including a point reflection among...
    21 KB (2,742 words) - 08:37, 30 April 2025
  • Thumbnail for Symmetry (geometry)
    geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object...
    30 KB (3,496 words) - 07:42, 15 June 2024
  • Thumbnail for Symmetry
    larger portions. Other symmetries include glide reflection symmetry (a reflection followed by a translation) and rotoreflection symmetry (a combination of...
    36 KB (3,885 words) - 14:29, 23 March 2025
  • simultaneous flip in the sign of all three spatial coordinates (a point reflection): P : ( x y z ) ↦ ( − x − y − z ) . {\displaystyle \mathbf {P}...
    39 KB (5,164 words) - 10:18, 25 May 2025
  • Thumbnail for Dihedral group
    mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest...
    28 KB (3,499 words) - 03:21, 1 January 2025
  • Thumbnail for Rotational symmetry
    {\displaystyle {\tfrac {360^{\circ }}{n}}.} ⁠ Examples without additional reflection symmetry: n = 2, 180°: the dyad; letters Z, N, S; the outlines, albeit not...
    15 KB (1,606 words) - 06:43, 27 March 2025
  • Thumbnail for Symmetry group
    symmetry of X. The above is sometimes called the full symmetry group of X to emphasize that it includes orientation-reversing isometries (reflections...
    17 KB (2,283 words) - 19:34, 22 March 2024
  • Thumbnail for Wallpaper group
    patterns have more forms of symmetry, including some rotational and reflectional symmetries: Example A: Cloth, Tahiti Example B: Ornamental painting, Nineveh...
    65 KB (6,485 words) - 13:43, 16 April 2025
  • Thumbnail for Symmetry breaking
    has a continuous symmetry given by rotation about the axis through the top of the hill (as well as a discrete symmetry by reflection through any radial...
    14 KB (1,714 words) - 13:48, 17 April 2025
  • Thumbnail for Symmetry in biology
    folded in half. Symmetry is one class of patterns in nature whereby there is near-repetition of the pattern element, either by reflection or rotation. While...
    35 KB (4,100 words) - 22:22, 30 December 2024
  • Thumbnail for Octahedral symmetry
    (or orientation-preserving) symmetries, and 48 symmetries altogether. These include transformations that combine a reflection and a rotation. A cube has...
    29 KB (1,868 words) - 00:12, 22 March 2025
  • Thumbnail for Axial symmetry
    an axis. The main types of axial symmetry are reflection symmetry and rotational symmetry (including circular symmetry for plane figures). For example...
    1 KB (133 words) - 18:53, 6 March 2025
  • continuous symmetry is an intuitive idea corresponding to the concept of viewing some symmetries as motions, as opposed to discrete symmetry, e.g. reflection symmetry...
    3 KB (317 words) - 04:08, 14 April 2025
  • Decomino (section Symmetry)
    have an axis of reflection symmetry aligned with the gridlines. Their symmetry group has two elements, the identity and the reflection in a line parallel...
    3 KB (389 words) - 18:20, 18 January 2024
  • Thumbnail for Pentomino
    Pentomino (section Symmetry)
    has four axes of reflection symmetry, aligned with the gridlines and the diagonals, and rotational symmetry of order 4. Its symmetry group, the dihedral...
    18 KB (2,291 words) - 22:10, 3 May 2025
  • that is unchanged by a combination of rotation and reflection is said to have improper rotation symmetry. In 3 dimensions, improper rotation is equivalently...
    8 KB (815 words) - 20:44, 15 June 2024
  • Thumbnail for Octomino
    Octomino (section Symmetry)
    have an axis of reflection symmetry aligned with the gridlines. Their symmetry group has two elements, the identity and the reflection in a line parallel...
    5 KB (622 words) - 11:34, 16 March 2025
  • Thumbnail for Tetrahedral symmetry
    rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation. The group of all...
    18 KB (1,012 words) - 15:48, 25 April 2025
  • Thumbnail for Symmetry (physics)
    energy is preserved under a reflection in the y-axis. The last example above illustrates another way of expressing symmetries, namely through the equations...
    27 KB (3,283 words) - 17:51, 11 March 2025
  • ) through a centre of symmetry + / − {\displaystyle +/-} is the reflection symmetry along an arbitrary plane containing the internuclear axis For atoms...
    15 KB (1,766 words) - 20:56, 20 July 2023
  • Thumbnail for Kite (geometry)
    Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and two pairs...
    38 KB (3,800 words) - 16:41, 11 April 2025
  • Thumbnail for Isosceles triangle
    from the lengths of the legs and base. Every isosceles triangle has reflection symmetry across the perpendicular bisector of its base, which passes through...
    38 KB (4,157 words) - 08:26, 28 May 2025
  • Thumbnail for Heptomino
    Heptomino (section Symmetry)
    have an axis of reflection symmetry aligned with the gridlines. Their symmetry group has two elements, the identity and the reflection in a line parallel...
    6 KB (669 words) - 09:58, 4 February 2025
  • Thumbnail for Polyhex (mathematics)
    degrees rotation or reflection parallel or perpendicular to the long axis of the dihex (order 2 rotational and order 4 reflection symmetry), and the hexagon...
    6 KB (688 words) - 20:43, 3 February 2025
  • Thumbnail for Penrose tiling
    their lack of translational symmetry, Penrose tilings may have both reflection symmetry and fivefold rotational symmetry. Penrose tilings are named after...
    52 KB (5,991 words) - 22:48, 18 April 2025
  • Thumbnail for Tetromino
    diagonal reflection symmetry, and four-fold rotational symmetry T: vertical reflection symmetry only L: no symmetry S: two-fold rotational symmetry only One-sided...
    12 KB (1,174 words) - 03:12, 27 April 2025
  • Thumbnail for Icosahedral symmetry
    symmetry has 60 rotational (or orientation-preserving) symmetries and 60 orientation-reversing symmetries (that combine a rotation and a reflection)...
    49 KB (2,425 words) - 19:43, 25 April 2025
  • Thumbnail for Glossary of Sudoku
    reflection symmetry on one orthogonal axis. reflection symmetry on two orthogonal axes. reflection symmetry on one diagonal axis. reflection symmetry...
    17 KB (2,196 words) - 01:51, 13 May 2024