Summary: This study examines the geometric conditions of thrusters – the directions of which are fixed relative to the spacecraft – for realizing 3D attitude control using the minimum number of thrusters. The three controllable states for the attitude are defined as follows: arbitrary torques about three orthogonal axes; arbitrary torques about two of the orthogonal axes, and an identically zero torque about the third axis; and arbitrary torques about two of the orthogonal axes, and a unidirectionally positive or negative torque about the third axis. Four thrusters are used for the first state and three thrusters, for the other states. The study clarifies that three thrusters can control the 3D attitude of a spacecraft if a thruster can generate torque components opposite to those generated by the other two thrusters. A controller is designed for the third state and validated through numerical simulations.