Pivoting manipulation has such advantages as dexterity and safety over other methods to move bulky or heavy objects. In this paper we aim to show that an polyhedral object can be displaced to arbitrary position and orientation on a plane. For this purpose we analyze "small-time controllability (STC)" of pivoting operations and establish a motion planning algorithm. The manipulation motion is first planned as a path of a vehicile whose steering method has nonholonomic constraint and is then transformed into a pivoting operation sequence.