They look like interchangeable cam segments.
They seem to be slightly less than 90 deg. around the back of the large hole but, that might just be an effect of the photo angle.
Looking at how they seem to nest in the box I'm guessing they are all the same or at least the same in each box set.
The small knock through would determine  where the individual pieces would clock with each other when set on a common shaft.
Again, the way they sit in the boxes makes me think they are all the same.
Any chance of a picture of more than one part.

Yes they may all be the same size and shape but the only difference may be where the small clocking pin/hole is located on the face of the part.
It they are all the same then they will line up in only one practical way.
If each pin/hole were in a regularly spaced location that was a certain measured distance from one another, then there would be a great number of different combinations within each box assuming each box had a different series of segments in it.
How many boxes, of how many segments each, are there?

Does each segment have the partially punched through hole that leaves a pin protruding on the opposite side?
Or do some have the pin and some have a through hole with no pin?

Hmmm. Well from the wear marks on the faces, they seem to have been nesting together symmetrically for some time but I can't quite figure what they all do together unless they are weights or spacers used as a set for some purpose. 

Tell me again why you think these are related to a typewriter?

Next, I'm wondering why people think they are something other than a box of spare parts, only one or two of which would have a place in any given typewriter (or other machine, as the case may be). Why do we think they are all of a set? What did I miss?