rotation-reflection axis

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• Rotation matrix — In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example the matrix rotates points in the xy Cartesian plane counterclockwise through an angle θ about the origin of the Cartesian… …   Wikipedia

• Reflection (mathematics) — This article is about reflection in geometry. For reflexivity of binary relations, see reflexive relation. A reflection through an axis followed by a reflection across a second axis parallel to the first one results in a total motion which is a… …   Wikipedia

• Rotation group — This article is about rotations in three dimensional Euclidean space. For rotations in four dimensional Euclidean space, see SO(4). For rotations in higher dimensions, see orthogonal group. In mechanics and geometry, the rotation group is the… …   Wikipedia

• Rotation (mathematics) — Rotation of an object in two dimensions around a point O. In geometry and linear algebra, a rotation is a transformation in a plane or in space that describes the motion of a rigid body around a fixed point. A rotation is different from a… …   Wikipedia

• Improper rotation — In 3D geometry, an improper rotation, also called rotoreflection or rotary reflection is, depending on context, a linear transformation or affine transformation which is the combination of a rotation about an axis and an inversion about the… …   Wikipedia

• Point reflection — In geometry, a point reflection is a type of isometry of Euclidean space. It is a reflection whose mirror is a single point. An object that is invariant under a point reflection is said to possess point symmetry.In two dimensions, a point… …   Wikipedia

• Glide reflection — In geometry, a glide reflection is a type of isometry of the Euclidean plane: the combination of a reflection in a line and a translation along that line. Reversing the order of combining gives the same result. Depending on context, we may… …   Wikipedia

• Wick rotation — In physics, Wick rotation, named after Gian Carlo Wick, is a method of finding a solution to a problem in Minkowski space from a solution to a related problem in Euclidean space, by analytic continuation.It is motivated by the observation that… …   Wikipedia

• Principal axis theorem — In the mathematical fields of geometry and linear algebra, a principal axis is a certain line in a Euclidean space associated to an ellipsoid or hyperboloid, generalizing the major and minor axes of an ellipse. The principal axis theorem states… …   Wikipedia

• rotoflection axis — |rōd.ō|flekshən noun Etymology: rotoflection from roto + flection : a compound symmetry element that requires identity of the structure and form of a crystal with its former configuration after a combination of rotation of 60, 90, 120, or 180… …   Useful english dictionary

• Symmetry combinations — This article discusses various symmetry combinations.In 2D, mirror image symmetry in combination with n fold rotational symmetry, with the center of rotational symmetry on the line of symmetry, implies mirror image symmetry with respect to lines… …   Wikipedia