A method of working a polygon enabling a polyhedron to be formed on a work in such a way that a specific part of the polyhedron exactly agrees with a specified peripheral direction position on the work, wherein, in such a state that a tool blade is adapted to face a work peripheral direction position deviating from a specified position thereof as much as the difference between a first positional deviation (PE1), which accrues during a period from the start of rotation of a first main shaft (3a) having the work (1) mounted thereon to the time when the first and second main shafts (3a, 3b) reach normal running condiditons in which the both shafts rotate at a fixed ratio of speed, and a second positional deviation (PE2) which accrues during a period from the start of rotation of the second main shaft having the tool mounted thereon to the time of normal running condition, the rotation of the work and tool are started at the same time and, when a normal running condition is reached, feeding of the tool is started.