In order to investigate their reciprocal relationship, wedge impressions and writing tips are first to be scrutinised as they were pure geometrical objects. The former is then to be viewed as a tetrahedron, the latter as a polyhedral cone. Within the terminological framework used here, the three edges of the wedge which lay on the tablet surface will be called “outer edges”, the other ones “inner edges”. The fundamental element in this system is the “directional edge”, or “spine”, of the wedge. The spine is defined as the wedge’s edge that is left behind by the blade of the stylus when it is impressed into the soft clay. The determination of the spine is thus independent from other variables, like length or incline, which are exposed to secondary and partially unpredictable influences. Therefore, the spine will always be the vertical, horizontal and “NW-SE” oblique inner edge in the case of vertical wedges, horizontal wedges, and oblique wedges / Winkelhaken respectively. This assures that the subsequent analysis is based on a primary correspondence between writing tip and wedge impressions. The orientation of the spine determines the positioning of all other wedge elements as illustrated in the figure below (download here): inner and outer edges and inner and outer angles.

Similarly, the stylus’ edges corresponding to the right and left inner edges will be called “right” and “left” edge respectively.

Additional elements relevant to the geometric characterization of cuneiform script can be derived from the primary wedge components. Of particular interest are the following:

The stylus, manipulated by hand and fingers, undergoes a number of movements during the writing process. Some of these movements are necessary to write different types of wedges, whereas other ones depend on the scribe’s writing style and attitude, and others are simply accidental. All of them influence the final appearance of the wedge. The following discussion will focus neither on accidental movements nor on those due to special conditions and constraints – e.g. writing on the edges of the tablet – but rather on basic movements which are coherently performed by the scribe while writing a tablet. Since we cannot observe ancient scribes at work, such movements are best investigated through the lens of the wedges left behind by the stylus. As a frame of reference, the writing surface will be treated as a plane, and a cartesian coordinate system will be defined, the XY axes of which lay on the tablet plane, the X axis being parallel to the (abstracted) line direction. Within this system, it is possible to define the position of the stylus at any time through three angles:

(1) Horizontal tilt, namely the angle between the “blade” of the stylus and the YZ plane: determines the wedge’s orientation on the tablet surface, distinguishing between horizontals, verticals and Winkelhaken;

(2) Vertical tilt, namely the angle between the blade of the stylus and the XY plane: determines the wedge’s “slope”, distinguishing e.g. oblique wedges from Winkelhaken; it is inversely proportional to the wedge’s length;

(3) Lateral tilt, namely the stylus’ rotation around the axis of its blade: determines the variation of the aperture angle’s tilt, i.e. whether the wedge “hangs” toward its right or left face or is “symmetrical” to the tablet surface (the apertural angle’s tilt is defined through the angle between the bisector of the wedge’s aperture angle and the perpendicular to the XY plane).