![]() If the translation vector of a glide reflection is itself an element of the translation group, then the corresponding glide reflection symmetry reduces to a combination of reflection symmetry and translational symmetry. ![]() It is isomorphic to a semi-direct product of Z and C 2.Ī 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.įor any symmetry group containing some glide reflection symmetry, the translation vector of any glide reflection is one half of an element of the translation group. 6 (glide-reflections, translations and rotations) is generated by a glide reflection and a rotation about a point on the line of reflection. If that is all it contains, this type is frieze group p11g.Įxample pattern with this symmetry group:įrieze group nr. In the case of glide reflection symmetry, the symmetry group of an object contains a glide reflection, and hence the group generated by it. Ĭombining two equal glide reflections gives a pure translation with a translation vector that is twice that of the glide reflection, so the even powers of the glide reflection form a translation group. ![]() The isometry group generated by just a glide reflection is an infinite cyclic group. This isometry maps the x-axis to itself any other line which is parallel to the x-axis gets reflected in the x-axis, so this system of parallel lines is left invariant. These are the two kinds of indirect isometries in 2D.įor example, there is an isometry consisting of the reflection on the x-axis, followed by translation of one unit parallel to it. Thus the effect of a reflection combined with any translation is a glide reflection, with as special case just a reflection. However, a glide reflection cannot be reduced like that. The combination of a reflection in a line and a translation in a perpendicular direction is a reflection in a parallel line. It can also be given a Schoenflies notation as S 2∞, Coxeter notation as, and orbifold notation as ∞×. A glide reflection can be seen as a limiting rotoreflection, where the rotation becomes a translation. In group theory, the glide plane is classified as a type of opposite isometry of the Euclidean plane.Ī single glide is represented as frieze group p11g. The intermediate step between reflection and translation can look different from the starting configuration, so objects with glide symmetry are in general, not symmetrical under reflection alone. In 2-dimensional geometry, a glide reflection (or transflection) is a symmetry operation that consists of a reflection over a line and then translation along that line, combined into a single operation. The operation of a glide reflection: A composite of a reflection across a line and a translation parallel to the line of reflection Since this footprint trail has glide reflection symmetry, applying the operation of glide reflection will map each left footprint into a right footprint and each right footprint to a left footprint, leading to a final configuration which is indistinguishable from the original. ( December 2016) ( Learn how and when to remove this template message) ![]() Please help improve it to make it understandable to non-experts, without removing the technical details. They will be able to use rotational symmetry when describing a shape's properties.This article may be too technical for most readers to understand. They will be taught to identify how many times a shape can be rotated around a centre point and remain the same. In Year 6 some more able children will also look at rotational symmetry (generally taught in Y7). This is often combined with coordinates work. They will be given a shape and asked to reflect in the other three quadrants using the x-axis and y-axis. Or they may be asked to reflect whole shapes in a mirror line. For example, they may be given half a shape and asked to complete it using the mirror line. In Year 5 children are taught to reflect shapes and patterns in lines that are parallel to the axis. They will often use squared paper to do this task. They will become aware that shapes may have more than one line of symmetry and complete investigations about how many lines of symmetry shapes have.Ĭhildren will also learn to draw symmetrical patterns with respect to a specific line of symmetry. In Year 4 children identify lines of symmetry in 2D shapes. In Year 3 children are taught to sort shapes into symmetrical and non-symmetrical polygons. They may be given the shapes and asked to fold them or draw on a line of symmetry. In Year 2 children will be introduced to the concept of symmetry and taught to identify line symmetry in a vertical line.
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