In geometry, the symmetry set is a method for representing the local symmetries of a curve, and can be used as a method for representing the shape of objects...

Symmetry (from Ancient Greek συμμετρία (summetría) 'agreement in dimensions, due proportion, arrangement') in everyday life refers to a sense of harmonious...

subset of the symmetry set, which is defined similarly, except that it also includes circles not contained in S. (Hence, the symmetry set of S generally...

orientation-preserving) symmetries, and 48 symmetries altogether. These include transformations that combine a reflection and a rotation. A cube has the same set of symmetries...

to have more than one line of symmetry. The types of symmetries that are possible for a geometric object depend on the set of geometric transforms available...

or a crystal, a symmetry element corresponds to a set of symmetry operations, which are the rigid transformations employing the symmetry element that leave...

has icosahedral symmetry if it has the same symmetries as a regular icosahedron. Examples of other polyhedra with icosahedral symmetry include the regular...

molecular symmetry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a...

object remains unchanged under a set of operations or transformations. Given a structured object X of any sort, a symmetry is a mapping of the object onto...

In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group...

regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection...

The symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under...

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

translational symmetry is the invariance of a system of equations under any translation (without rotation). Discrete translational symmetry is invariant...

centers of all bi-tangent circles form the symmetry set. The medial axis is a subset of the symmetry set. Rutter, J. W. (2000), Geometry of Curves, CRC...

the plane, the set of plane symmetries that preserve the pattern forms a group. The groups that arise in this way are plane symmetry groups and are of...

annihilate. The symmetry set of a curve has endpoints at the cusps corresponding to the vertices, and the medial axis, a subset of the symmetry set, also has...

Time-translation symmetry or temporal translation symmetry (TTS) is a mathematical transformation in physics that moves the times of events through a...

Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law...

of mass. If the set of fixed points of the symmetry group of an object is a singleton then the object has a specific centre of symmetry. The centroid and...

naturally in the study of symmetries and geometric transformations: The symmetries of an object form a group, called the symmetry group of the object, and...

crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices...

discrete symmetry is a symmetry that describes non-continuous changes in a system. For example, a square possesses discrete rotational symmetry, as only...

Origin of Symmetry is the second studio album by the English rock band Muse, released on 18 June 2001 through Taste Media. It was produced by John Leckie...

global symmetry. Local symmetry, the cornerstone of gauge theories, is a stronger constraint. In fact, a global symmetry is just a local symmetry whose...

X is a set; for matrix groups, X is a vector space. The concept of a transformation group is closely related with the concept of a symmetry group: transformation...

have the same symmetries, regardless of the designs' superficial details; whereas C has a different set of symmetries. The number of symmetry groups depends...

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

in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms...

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....