Yours sounds like a knife file.

There are a few different types of files that are triangular. There are three-square files, knife files, and warding files. They can be Swiss pattern or American.

For filing threads, I'd use a three-square, American (single-cut) file. I'd use this type of file because the three-square file has 60 degree corners, and it will preserve the thread profile.

Here's a link to the Nicholson book on files from the 19th century which  I would give to all my students to learn about files and filing:

https://archive.org/details/atreatiseonfile00provgoog/page/n1/mode/2up