I have data that is organized in kind of a "key-key" format, rather than "key-value". It's like a HashMap, but I will need O(1) lookup in both directions. Is there a name for this type of data structure, and is anything like this included in Java's standard libraries? (or maybe Apache Commons?)
I could write my own class that basically uses two mirrored Maps, but I'd rather not reinvent the wheel (if this already exists but I'm just not searching for the right term).
There is no such class in the Java API. The Apache Commons class you want is going to be one of the implementations of BidiMap.
As a mathematician, I would call this kind of structure a bijection.