This paper focuses on the numerical simulation of the motion of regular shaped ice particles under the forces and torques generated by aerodynamic loading. Ice particles can occur during landing and take-off of aircraft at ground level up to the stratosphere at cruising altitude. It may be expected that the particle Reynolds number is high because the flow around the aircraft is in certain regions characterized by strong acceleration and deceleration of the flow. In combination with this flow pattern, the rotation of particles becomes important. Applicable translational and rotational equations of motion combined with a drag correlation taking into account rotation will be derived for a Lagrangian type particle tracking. Orientation is described with quaternions to prevent the singularities associated with the description by Euler angles. The influence of regular shaped particles on collection efficiencies is investigated. Test cases are the flow past a cylinder, a NACA0012 airfoil and a NHLP L1/T2 three element airfoil. Due to the increased computational effort compared to the purely translational approach, observed trajectory simulation times are reported.