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A typical example of glide reflection in everyday life would be the track of footprints left in the sand by a person walking on a beach. Frieze group nr. 6 (glide-reflections, translations and rotations) is generated by a glide reflection and a rotation about a point on the line of reflection. It is isomorphic to a semi-direct product of Z and C 2.
p2mm: TRHVG (translation, 180° rotation, horizontal line reflection, vertical line reflection, and glide reflection) Formally, a frieze group is a class of infinite discrete symmetry groups of patterns on a strip (infinitely wide rectangle), hence a class of groups of isometries of the plane, or of a strip.
*Schönflies's point group notation is extended here as infinite cases of the equivalent dihedral points symmetries § The diagram shows one fundamental domain in yellow, with reflection lines in blue, glide reflection lines in dashed green, translation normals in red, and 2-fold gyration points as small green squares.
Both behavioural and neurophysiological studies have confirmed the special sensitivity to reflection symmetry in humans and also in other animals. [28] Early studies within the Gestalt tradition suggested that bilateral symmetry was one of the key factors in perceptual grouping. This is known as the Law of Symmetry. The role of symmetry in ...
glide-reflection, i.e. reflection followed by translation. All translations which occur are assumed to form a discrete subgroup of the group symmetries being described. Each group is denoted in orbifold notation by a finite string made up from the following symbols:
reflection with respect to a plane, and a translation in that plane, a rotation about an axis perpendicular to the plane, or a reflection with respect to a perpendicular plane; glide reflection with respect to a plane, and a translation in that plane; inversion in a point and any isometry keeping the point fixed
Cognitive shifting is the core process of all meditation, especially in Kundalini meditation but also in Zen meditation and even in Christian mysticism where the mind's attention is re-directed (or shifted) toward particular theologically-determined focal points. Recent books have spoken directly of cognitive shifting as a meditative procedure.
The cortical midline structure is extremely important in the understanding of the self, especially during the task of self-reflection. Many researchers believe that self-reference plays a role in the expression of psychoses. The disturbance of the individual's self may be underlying the manifestation of these psychoses.