Proteins are the workhorse molecules of the cell, which are obtained by folding long chains of amino acids. Since not all shapes are obtained as a folded chain of amino acids, there should be global geometrical constraints on the shape. Moreover, since the function of a protein is largely determined by its shape, constraints on the shape should have some influence on its interaction with other proteins. In this paper, we consider global geometrical constraints on the shape of proteins. Using a mathematical toy model, in which proteins are represented as closed chains of tetrahedrons, we have identified not only global geometrical constraints on the shape of proteins, but also their influence on protein interactions. As an example, we show that a garlic-bulb like structure appears as a result of the constraints. Regarding the influence of global geometrical constraints on interactions, we consider their influence on the structural coupling of two distal sites in allosteric regulation. We then show the inseparable relationship between global geometrical constraints and protein interactions; i.e. they are different sides of the same coin. This finding could be important for the understanding of the basic mechanisms of allosteric regulation of protein functions.