In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure...

transformation, it is said to have symmetry, and the transformation is called a symmetry operation. Glide-reflection symmetry is seen in frieze groups (patterns...

geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object...

point reflection is said to possess point symmetry (also called inversion symmetry or central symmetry). A point group including a point reflection among...

larger portions. Other symmetries include glide reflection symmetry (a reflection followed by a translation) and rotoreflection symmetry (a combination of...

simultaneous flip in the sign of all three spatial coordinates (a point reflection): P : ( x y z ) ↦ ( − x − y − z ) . {\displaystyle \mathbf {P}...

mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest...

symmetry of X. The above is sometimes called the full symmetry group of X to emphasize that it includes orientation-reversing isometries (reflections...

{\displaystyle {\tfrac {360^{\circ }}{n}}.} ⁠ Examples without additional reflection symmetry: n = 2, 180°: the dyad; letters Z, N, S; the outlines, albeit not...

an axis. The main types of axial symmetry are reflection symmetry and rotational symmetry (including circular symmetry for plane figures). For example...

(or orientation-preserving) symmetries, and 48 symmetries altogether. These include transformations that combine a reflection and a rotation. A cube has...

patterns have more forms of symmetry, including some rotational and reflectional symmetries: Example A: Cloth, Tahiti Example B: Ornamental painting, Nineveh...

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...

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...

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...

that is unchanged by a combination of rotation and reflection is said to have improper rotation symmetry. In 3 dimensions, improper rotation is equivalently...

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...

rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation. The group of all...

by reflection in a plane mirror; it is of the same size as the original object, yet different, unless the object or figure has reflection symmetry (also...

energy is preserved under a reflection in the y-axis. The last example above illustrates another way of expressing symmetries, namely through the equations...

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...

no symmetry (C1), reflection symmetry (Cs), 2-fold rotational symmetry (C2), and central point symmetry (Ci). There are four infinite cyclic symmetry families...

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...

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...

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...

1D is a simple reflection. It can be represented by the simplest Coxeter group, A1, [ ], or Coxeter-Dynkin diagram . Affine symmetry groups represent...

In 2D, the symmetry group Dn includes reflections in lines. When the 2D plane is embedded horizontally in a 3D space, such a reflection can either be...

has four axes of reflection symmetry, aligned with the gridlines and the diagonals, and rotational symmetry of order 4. Its symmetry group, the dihedral...

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...

from the lengths of the legs and base. Every isosceles triangle has reflection symmetry across the perpendicular bisector of its base, which passes through...