New bound in continuum states and long-lived resonances in one photonic triangular pyramid with two semi-infinite leads are reported, together with general theorems giving their existence conditions. The pyramid is composed of connected open loops (of length L). When bound in continuum states exist within state continua, they induce long-lived resonances for specific values of some modified lengths of the 6 open loops constituting the pyramid. This enables to tune these resonances by means of these lengths. The results obtained in this work take due account of the state number conservation between the final system and the reference one constituted by the independent pyramid and semi-infinite leads. The respect of this conservation enables to find all the states of the final system and among them the bound in continuum ones. This is one of the originalities of this work. The other new general results are the different sets of bound in continuum states and long-lived resonances, as well as the theorems giving their existence conditions. These results may have a big impact on general investigations of bound in continuum states, long-lived resonances and communication technology improvements.