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Pentacube Nomenclature

A lot of people use different pentacube nomenclature. Here, I am listing my pentacube nomenclature.

Listed above are the 29 one-sided pentacubes. I like to identify free polyforms, so I will refer to them as the 23 pentacubes, with the bottom 6 having their mirror images merged.
For the top 12, they are the pentominoes, so they will get their pentomino letter.
From left to right, first row: F, I, L, Y, V, T
Second row: W, X, P, U, Z, N
The remaining 11 will be named according to two letters. They look like two pentominoes with certain portions rotated. Those two letters are its name, in alphabetical order. Here are the first five according to this system, with "_" meaning it is not part of the first five.
Third row, left to right: TY, _, PT, _, _
Fourth row: _, UZ, NP
Fifth row: _, PW, _
2 of the remaining six would have their name be the same. Three of the other four have only one pentomino, and the last has four pentominoes.
I've decided to name the last two on the third row Q and A, and name the first one of rows four and five FP and PF accordingly. I named the second from the left on the third row "TB" standing for T-Branch, and the last one on the last row "CH" for Chiral.
And there you have it, my pentacube nomenclature! Home