The local topography of a conical intersection can be represented by four parameters, readily determined from multireference configuration interaction wave functions, describing the pitch and tilt of the double cone. The time-dependent Schrodinger equation is solved in the vicinity of a conical intersection in the adiabatic basis using an approach tailored to this representation. It is shown that an adiabatic state treatment, which offers conceptual advantages is, in the appropriate set of internal coordinates, not qualitatively more difficult than the equivalent calculation in a diabatic basis. The present treatment is fully hermitian and takes full account of the geometric phase effect being, for example, gauge invariant (in the infinite basis limit) and could be used to develop a fully adiabatic description of nonadiabatic dynamics. The gauge invariant formulation provides interesting insights into the consequences of neglecting the geometric phase. The algorithm is used to study the effects of the double cone's topography on the outcome of a nonadiabatic transition. Transitions from both the upper state to the lower state and from the lower state to upper state are considered for representative sets of conical parameters. The effects of the local topography on the outcome of nonadiabatic transitions can be dramatic. (C) 2001 American Institute of Physics.