In the near future, it will be possible to perform coincidence detection on a gamma camera with three heads, which increases the geometric sensitivity of the system. Different geometric configurations are possible, and each configuration yields a different geometric sensitivity. The purpose of this work was to calculate the sensitivities for different three-headed configurations as a function of the position in the field of view, the dimensions of the detector heads and the distance of the heads from the center of the field of view. The configurations that were compared are: a regular two headed configuration (180 deg. opposed), a triple-headed configuration with the three heads in an equilateral triangle (120 deg.), and a triple-headed configuration with two heads in a regular two headed configuration, and the third perpendicular between the first two, which makes a U-shaped configuration. An expression was derived for any planar detector configuration to calculate the geometric sensitivity for each Line Of Response (LOR). This sensitivity was integrated to get the sensitivity profile, which gives the geometric sensitivity at a certain distance from the center of rotation. We found that the triangular configuration gave the best sensitivities when placed very near to each other (nearly full ring configuration), but for larger fields of view, the U-shaped configuration performed better.