Using a rule as a gauge, I observed on the surface of the shell four very thin tangeing lines in an almost diagonal direction that are straight and flat over a distance of about 2 inches, and situated more or less symetrically between the longitudinal and transverse axes of the instrument. This "observation" can easily be verified by inspecting any existing instrument of the violin family. The exact locations of these four rectilinear cross sections (flat surface) are found just where the profile of the shell changes from convex to concave in each quadrant. It occured to me to adopt a crucial mechanical and constructional function for these "thinly rectilinear lines" by regarding them as extremely narrow "elements" which come into motion at some special frequency. In this assuming condition the "elements" are regarded as not being part of the compound shell. In that state the vibration of these "elements" puts the air in the box in motion at four places which is the sound transmitting medium. When a single "element" is regarded as a string it will come into motion at some special frequency(ies), when its characteristic frequency coincides with the frequency of the played tone on a string, like a resonance string on some special instruments. The "contributing area" of the shell acting upon the air in the box by the number of equal elements, one in each quadrant, is increased and thus the euphonious result. Additionally adjacent radial cross-sections, regarded as a "fan-shaped pattern" of "gradually differentiating curved elements", arranged dually in the upper and lower quadrants, would come into motion at a continuous spectrum of specific frequencies. Since there are an infinite number of differently shaped "elements" in each quadrant, the frequency range of the shell is optimized as well as the participating part of the shell. Conversely it becomes possible to transform a specific frequency to the air when a string is attacked giving a certain frequency and the corresponding elements comes into motion thereby transforming the vibration of the string via those "elements" to the air in the violin box. The volume level and the sound spectrum of the instrument might be dependent on the moving mass; since there are, theoretically, always four equal "elements", the moving mass of the shell is increased along with its ability to act upon the air, which is the sound-supporting medium. Furthermore those "elements" may contribute to the "gradual distribution of tension on the shell" when the sound post is put into the instrument, thus streching the "elements" (shell) outwards. The stretched "elements" act like strings and the tension in the compound shell makes it possible to vibrate like a string. This extremely simplified idea of function and construction is the basis of my effort to find a solid geometric structure of the instruments shell. I'm aware that the real function is far more complicated and different but as a construction idea forfinding an underlying 3D geometric model it was worth a try. I adopted this admittedly simplified model solely as a starting point for my attempt to identify an underlaying geometric concept, without necessarily defining the instrument scientifically. For a comparison, I have examined the drawings by Sacconi (1#) and found incomplete "fan sectors" with dually arranged "elements", which are symmetrical in layout on a somewhat rotated transverse axis. Sacconi must have had a notion of a construction idea since he partly adapted the equal "element" layout in his iso line layout, assuming them as the average proportion of the Stradivarius arch shape. The Sacconi shells seemed to be a good starting point in the search for a geometric description.