Inside corner plane – where would one use this?

This is a core box plane. Believe it or not, it is used to plane a cylindrical depression! Go drive two nails into a piece of wood a few inches apart and place a framing square, try-square, or just a squared piece of wood against the two nails. Put a pencil tip at the corner of the square, where the handle meets the blade. Now move the square to all the positions it can engage the nails. You will find that the pencil traces out a circle. If you take the core box plane and run it along two rails, you have the same principle, where the rails take the role of the two nails. The tip of the cutter will traverse a circle plowed across the material. I’ve not used one, but I think they would hog out the material with other tools and use the core box to refine the result.

Why do this? For casting metal parts. You’ll need to look it up because it’s not something I know much about. I once worked with a guy that was a pattern maker before the steel industry died. He could have told you. By the time I knew him, he was doing landscaping and odd jobs.

A further discussion is here

Blood and Gore

Note the three versions start their numbering right after the monstrous Stanley #55, and are every bit as useful in the average shop.

Yours doesn’t look like a Stanley model, but I’ve only ever seen a couple.