This is a replacement knob for a ceiling fan, attic fan, or the shrouds of those fans. It fits on to a wall-plate-mounted rotary switch, similar to that of a light switch, but instead of a light switch there's a rotating head.

It fits on to mine, at least. I'm not sure if there's a standard size for this sort of item, or if mine's just proprietary. Here, why don't you go measure yours first?

The shape of the rotating axle should be like a circle truncated on two parallel sides. The circle diameter should be roughly 6mm and the distance between either truncated end to the other should be about 5.25mm, give or take a little. It is a press fit, so it won't matter much if it's off by about 0.05mm or so.

Hope this model can save someone some work!