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, 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 to carry out second polygon machining by the polygon cutter after the machining by the tool other than the polygon cutter, and carrying out machining on the workpiece by synchronously rotating the main shaft and the tool spindle to maintain a phase relationship between the main shaft and the tool spindle, wherein the control unit includes a synchronization ratio changing unit, characterized in that - the synchronization ratio changing unit is configured to change a synchronization ratio between a synchronization ratio necessary for the first or second polygon machining and a second synchronization ratio in which the main shaft can rotate at a rotation speed necessary for the machining by the tool other than the polygon cutter after the first polygon machining by rotating the tool spindle at a rotation speed not exceeding a maximum rotation speed, and - the control unit is configured so as to carry out the machining by the tool other than the polygon cutter by synchronously rotating the main shaft and the tool spindle in the second ratio after the first polygon machining and to carry out the second polygon machining by changing the synchronous ratio after the machining by the tool other than the polygon cutter after the first polygon machining. - 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, 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 to carry out second polygon machining by the polygon cutter after the machining by the tool other than the polygon cutter, and carrying out machining on the workpiece by synchronously rotating the main shaft and the tool spindle to maintain a phase relationship between the main shaft and the tool spindle, wherein the control unit includes a synchronization ratio changing unit, characterized in that - the synchronization ratio changing unit is configured to change a synchronization ratio between a synchronization ratio necessary for the first or second polygon machining and a second synchronization ratio in which the main shaft can rotate at a rotation speed necessary for the machining by the tool other than the polygon cutter after the first polygon machining by rotating the tool spindle at a rotation speed not exceeding a maximum rotation speed, and - the control unit is configured so as to carry out the machining by the tool other than the polygon cutter by synchronously rotating the main shaft and the tool spindle in the second ratio after the first polygon machining and to carry out the second polygon machining by changing the synchronous ratio after the machining by the tool other than the polygon cutter after the first polygon machining.