I'm shocked that I couldn't find an answer to this anywhere, but I have a situation where I have to categorize isosceles triangles by whether their legs are (individually) longer or shorter than their base. E.G. 3-3-2 vs. 3-3-4. Another way of looking at it is if the vertex angle is either less than 60°(for longer legs) or greater than 60°(for shorter legs).
I've taken to calling these "Tall" and "Wide" Isosceles respectively, but I was hoping for some official designation. Unfortunately, google only returns the elementary-level definitions of isosceles/equilateral/scalene and acute/obtuse.
However, I simply cannot believe that this never was considered and classified by some ancient greek philosopher, or that if their works did not survive that it wasn't later rediscovered by a renaissance mathematician. So, if the names exist, what are they?
For extra context, this is for something I'm doing on a computer where I classify triangles by sorting the edge lengths (descending) and then compare them: if the longest two are equal it's "tall", if the shortest two are equal it's "wide"; if both wide and tall it's equilateral, if neither it's scalene.