My best guess is that your basic assumption, that all pepper fragments have different shapes, is wrong.
The water is indented at the pepper fragment because gravity acts on it downward. Without surface tension the pepper would sink because of that. The surface tension of the water-air interface however, is strong enough to withstand the force downwards, resulting in a force balance, but at the cost of a certain degree of curvature. (see also this Physics.SE question)
The indentation of the water is a response to the gravitational pull on the pepper fragment, therefore the only reason for the triangular symmetry that you observe can be the shape of the pepper fragment. Apparently these fragments are all (roughly) triangular, which might be a consequence of the specific way that they were ground.