A polygon machining device comprising - a main shaft gripping a workpiece, - a tool spindle to which a polygon cutter is mounted, and - a control unit configured to control the rotation of the main shaft and the tool spindle, and being configured so as to carry out machining by a tool other than the polygon cutter on the workpiece after carrying out first polygon machining by the polygon cutter and carry out second polygon machining by the polygon cutter after the machining by the tool other than the polygon cutter, characterized in that - the control unit includes: a synchronization stopping unit configured to stop the main shaft in a predetermined fixed rotation position in a state where the main shaft and the tool spindle are synchronously rotated at the time of the first polygon machining when the first polygon machining ends; a synchronization releasing unit configured to release synchronization between the main shaft and the tool spindle when the machining by the tool other than the polygon cutter after the first polygon machining starts; a main shaft stopping unit configured to stop the main shaft in the fixed rotation position when the machining by the tool other than the polygon cutter after the first polygon machining ends; and a synchronization starting unit configured to synchronously rotate the main shaft and the tool spindle when the second polygon machining starts; and - the control unit is configured so as to end the first polygon machining in the state where the synchronization stopping unit is in operation, to start the machining by the tool other than the polygon cutter after the first polygon machining by operating the synchronization releasing unit, to end the machining by the tool other than the polygon cutter after the first polygon machining in the state where the main shaft stopping unit is in operation, and to carry out the second polygon machining by operating the synchronization starting unit. - a main shaft gripping a workpiece, - a tool spindle to which a polygon cutter is mounted, and - a control unit configured to control the rotation of the main shaft and the tool spindle, and being configured so as to carry out machining by a tool other than the polygon cutter on the workpiece after carrying out first polygon machining by the polygon cutter and carry out second polygon machining by the polygon cutter after the machining by the tool other than the polygon cutter, characterized in that - the control unit includes: a synchronization stopping unit configured to stop the main shaft in a predetermined fixed rotation position in a state where the main shaft and the tool spindle are synchronously rotated at the time of the first polygon machining when the first polygon machining ends; a synchronization releasing unit configured to release synchronization between the main shaft and the tool spindle when the machining by the tool other than the polygon cutter after the first polygon machining starts; a main shaft stopping unit configured to stop the main shaft in the fixed rotation position when the machining by the tool other than the polygon cutter after the first polygon machining ends; and a synchronization starting unit configured to synchronously rotate the main shaft and the tool spindle when the second polygon machining starts; and a synchronization stopping unit configured to stop the main shaft in a predetermined fixed rotation position in a state where the main shaft and the tool spindle are synchronously rotated at the time of the first polygon machining when the first polygon machining ends; a synchronization releasing unit configured to release synchronization between the main shaft and the tool spindle when the machining by the tool other than the polygon cutter after the first polygon machining starts; a main shaft stopping unit configured to stop the main shaft in the fixed rotation position when the machining by the tool other than the polygon cutter after the first polygon machining ends; and a synchronization starting unit configured to synchronously rotate the main shaft and the tool spindle when the second polygon machining starts; and a main shaft stopping unit configured to stop the main shaft in the fixed rotation position when the machining by the tool other than the polygon cutter after the first polygon machining ends; and a synchronization starting unit configured to synchronously rotate the main shaft and the tool spindle when the second polygon machining starts; and - the control unit is configured so as to end the first polygon machining in the state where the synchronization stopping unit is in operation, to start the machining by the tool other than the polygon cutter after the first polygon machining by operating the synchronization releasing unit, to end the machining by the tool other than the polygon cutter after the first polygon machining in the state where the main shaft stopping unit is in operation, and to carry out the second polygon machining by operating the synchronization starting unit.