Regular System of Points

(mathematics), an infinite set of points in a plane (or in space) satisfying the following conditions: (1) there exists a radius R such that any circle in the plane (sphere in space) of radius R contains at least one point of the system (homogeneity condition); (2) there exists a radius r> 0 such that a circle (sphere) of this radius described around a point in the system contains no other points in the system; and

Figure 1. Regular system of points in a plane

(3) for any two points A and B of the system, there exists a motion (seeMOTION [mathematics]) that maps the system onto itself and A onto B. An example of a regular point system is given in Figure 1.