I think this thread is diverging into confusingly talking about quite different tools – for quite different purposes too!
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The OP is describing a Filing Rest, a lathe attachment used for filing flats on a turned end of the work-piece.
It guides the file by it running without sliding, on two freely-rotating rollers on a yoke of adjustable height, straddling the work from below. It allows creating polygons, in conjunction with a suitable dividing arrangement on the lathe spindle.
Hardened rollers should not hurt a good-quality file, provided they do revolve freely and the file is not made to move diagonally. I think some people have used small, sealed ball-bearings races for the rollers.
Looking at Hemingway's catalogue, their Precision Filing-Rest rollers are flanged to guide the file's safe edge. This both keeps the file on track, at right-angles to the lathe axis, and gives repeated facet lengths.
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A Filing-Button as others describe is a template for filing arcs of its own radius.
A Button can be made to revolve (should be, if hardened) or be held rigidly to the work, usually by a screw (and nut) through the hole concentric with the intended arc, to aid forming the end of, for example, a motion-gear link.
It is meant to guide the filing, not the file, and if hardened it can soon lead to blunt files unless used with great care!
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I don't have a filing-rest but often use filing-buttons, and sometimes the work dimensions allow this to be no more than two ordinary washers, one each side of the work. If I hit them with the file, they don't harm the tool.