Turning pentagons on a lathe

[tonyfoale]

Flat as performed by a rotating cutter on the same axis, the amount dependent of width of face in question.

The rotating cutter has to be on a different axis or it can only cut circular shapes.

Not forever, but this capability is in multi-axis CNC lathes, though most run a mill on each face been around a while.
At any rate, those cutters are driven, timed with but not connected to main spindle .

When this technique is applied to manual machines the cutter spindle is connected to the main spindle through mechanical means to achieve the timing and appropriate gear ratio.