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In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. However, a set of four or more distinct points will, in general, not lie in a single plane.
The terms horizontal (h) and vertical (v), and the corresponding subscripts, refer to the additional mirror plane, that can be parallel to the rotation axis (vertical) or perpendicular to the rotation axis (horizontal). The simplest nontrivial axial groups are equivalent to the abstract group Z 2: C i (equivalent to S 2) – inversion symmetry
A plane mirror is a mirror with a flat reflective surface. [ 1 ] [ 2 ] For light rays striking a plane mirror, the angle of reflection equals the angle of incidence. [ 3 ] The angle of the incidence is the angle between the incident ray and the surface normal (an imaginary line perpendicular to the surface).
Points in a mirror plane are invariant under reflection, and hence the points on their intersection (a line: the axis of rotation) are invariant under both the reflections, and hence under the rotation. Another simple way to find the rotation axis is by considering the plane on which the points α, A, a lie.
Reflections, or mirror isometries, denoted by F c,v, where c is a point in the plane and v is a unit vector in R 2. (F is for "flip".) have the effect of reflecting the point p in the line L that is perpendicular to v and that passes through c. The line L is called the reflection axis or the associated mirror.
Since 6 generates 6 points, and 3 generates only 3, 6 should be written instead of 3 / m (not 6 / m , because 6 already contains the mirror plane m). Analogously, in the case when both 3 and 3 axes are present, 3 should be written. However we write 4 / m , not 4 / m , because both 4 and 4 generate four points.
All the labelled points, except D and E, are coplanar. They are in the plane of symmetry of the whole figure. This includes the point F, which is not mentioned above. It is defined and discussed below, in § Position of the focus. Let us call the length of DM and of EM x, and the length of PM y.
By convention, the axis of proper rotation of greatest order is defined as the principal axis. All other symmetry elements are described in relation to it. A vertical mirror plane (containing the principal axis) is denoted σ v; a horizontal mirror plane (perpendicular to the principal axis) is denoted σ h.