<p>The Triple Helix of innovation is a three-person cooperative game with transferable utility. The core is defined as the set of players’ utilities that ensures individual and collective interests and the constraints on these utilities. Geometrically, the core of the Triple Helix game is a polygon with at most six faces, meaning that it may have less. The paper responds the question on how does the core form. Starting with the geometrical construction of the core of an imaginary Triple Helix game with six faces, we computed the coordinates of the 12 intersections of the six pairwise lines bounding the core and the ones of the vectors of the perimeter of the core. To illustrate, publications and patents data were collected from the Web of Science and the United States Patents and Trademark Office databases. The rules of the games were determined and the cores plotted. Results showed that the length of the faces of the core depends on bilateral and trilateral interactions only, and so does the surface area of the core as measurement of the synergy within the considered innovation system. Moreover, each bilateral collaboration engenders one face of the core and, with the trilateral collaboration, contributes a second; consequently, when that bilateral collaboration vanishes the core loses a face and the length of the second face decreases, so does the synergy within the system. The theory of the Triple Helix stating that the interactions among innovation actors generates the synergy that leads to innovation is then confirmed. The more an interaction, the lengthier the side of the core it engenders.</p>