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When two cells in the Voronoi diagram share a boundary, it is a line segment, ray, or line, consisting of all the points in the plane that are equidistant to their two nearest sites. The vertices of the diagram, where three or more of these boundaries meet, are the points that have three or more equally distant nearest sites.
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
In the 5 cases of rotational symmetry of order 3 or 6, the unit cell consists of two equilateral triangles (hexagonal lattice, itself p6m). They form a rhombus with angles 60° and 120°. In the 3 cases of rotational symmetry of order 4, the cell is a square (square lattice, itself p4m).
A glide reflection line parallel to a true reflection line already implies this situation. This corresponds to wallpaper group cm. The translational symmetry is given by oblique translation vectors from one point on a true reflection line to two points on the next, supporting a rhombus with the true reflection line as one of the diagonals. With ...
This article summarizes the classes of discrete symmetry groups of the Euclidean plane. The symmetry groups are named here by three naming schemes: International notation, orbifold notation, and Coxeter notation. There are three kinds of symmetry groups of the plane: 2 families of rosette groups – 2D point groups; 7 frieze groups – 2D line ...
A circle is thus said to be symmetric under rotation or to have rotational symmetry. If the isometry is the reflection of a plane figure about a line, then the figure is said to have reflectional symmetry or line symmetry; [3] it is also possible for a figure/object to have more than one line of symmetry. [4]
A time–distance diagram is a chart with two axes: one for time, the other for location. The units on either axis depend on the type of project: time can be expressed in minutes (for overnight construction of railroad modification projects such as the installation of switches) or years (for large construction projects); the location can be (kilo)meters, or other distinct units (such as ...
The unit distance graph for a set of points in the plane is the undirected graph having those points as its vertices, with an edge between two vertices whenever their Euclidean distance is exactly one. An abstract graph is said to be a unit distance graph if it is possible to find distinct locations in the plane for its vertices, so that its ...