**R0**. A RIGE is developed in two dimensions, however, reliefs and holes are used to mark the designs.**R1**. Only figures limited by straight segments are considered. Curvilinear design can be used to fill elementary polygonal figures, to avoid rigidity,*dryness*and*too geometrical*forms. But they do not contradict the basic rectilinear criterion, which remains.**R2**. All these segments are parallel to a few directions in the plane, derived from the division of the compass (360 degrees) by an integer N. This integer is called the Order, and the N directions, the main directions. Direction 0 will be the Reference, and**q**=360º/N will be called the Basic Angle. Violations of this rule are exceptional, and will be considered in the*Metabolês*section below. They not, however, affect this very basic law.**R3**. All these segments are situated on specific straight lines, parallel to the main directions. The distances between those lines are always equal to a very small number of quantities, 1, 2 or 3, according to the order. These distances are not arbitrary, but are determined by this order and by the angles - all multiples of- between the main directions.**theta****R4**. The set of the N families of parallel straights is called the Lattice or Net of the form, briefly the N-lattice. All the segments belong to the Net; all the figures belong to the Net; the Net can be considered as the union or set of many possible RIGE forms of a given order.**R5**. The segments form closed polygonal figures, convex or not, symmetrical or not. Those without segments between them will be the Elementary Elements -EE- (elements in the lowest level), which, by juxtaposition, give larger figures.**R6**. Their sizes are not too different: a general aspect of constant density of lines can be observed (and measured), recalling a grid, or a*tissue*.**R7**. At least one point can be found which is a symmetry centre for all, or a part, of the form. The order of this central symmetry is equal to the order of the net to which the form belongs.**R8**. The segments which limits the figures are united in polygonal lines with a width, as frames or sheets, which are never interrupted: whether they are closed or whether they finish in the external limits of the figure (actual figures are always limited, while nets are infinite by nature).**R9**. The width of the frame is constant for the same form.**R10**. When frames intersect, only two do so at the same point. The angle is non-zero (and of course, equal to the angle between two main directions). Frames never bend at the intersection point, or, equivalently, opposite angles are equal.**R11**. The intersection is usually represented (from Arabic countries to the West) as in three dimensions: one frame covers the other.**R12**. When one frame (f1) covers another (f2) at a given intersection, at the following intersection it will be covered in turn by a third (f3) (which could be the second, f2).**R13**. The form can actually be constructed by means of physical frames, bent and interlaced according to the former rules. Simple figures (EE) appear as empty spaces between frames.**R14**. When the widths of frames are maxima, they fill the entire plane, with the disappearance of elementary figures. The aspect is now a polygonal chess board (damero), used in wood-work, musical instruments decoration, etc.