I've seen several different naming schemes used for pentominoes. This is

the system I'm using (I think only F & N require a bit of imagination)
FF I L N PP TTT U U V V W W W X X Y ZZ

FF I L NN PP T UUU V V W W X YY Z

F I L N P T V X X Y ZZ

I LL N Y

A 3x20 solution (the other solution is easily obtained by a rotation of

the section from the Z to the L inclusive)
UUXPPPZYYYYWTFNNNVVV UXXXPPZZZYWWTFFFNNLV UUXIIIIIZWWTTTFLLLLV
A 4x15 solution
IIIIINNLLLLTVVV UUXNNNFZZWLTTTV UXXXYFFFZWWTPPV UUXYYYYFZZWWPPP

2 5x6 rectangles. Joined side-to-side, end-to-end, or stacked, these

enable construction of the 6x10 & 5x12 rectangles, and the 2x5x6 prism
NFVVV YYYYI NFFFV LLYZI NNFXV LZZZI PNXXX LZWTI PPUXU LWWTI PPUUU WWTTT

The 2x3x10 and 3x4x5 solutions are tricky to show - I hope these diagrams make sense:

A 2x3x10 solution (shown as 2 layers; Y and L are shared between the

2 layers)
VVVZIIIIIF UUXTTTWWPP VZZZNNNFFF UXXXTWWPPP VZYYYYNNFL UUXYTWLLLL
A 3x4x5 solution (3 layers, V F W & L shared between 2 or more layers)
VUUXF VZFFF VNYFW VUXXX TZZZW NNYPW VUUXW TTTZW NYYPP IIIII TLLLL NLYPP

--

| The effort to understand the universe is one of the very few things | | that lifts human life above the level of farce, and gives it some | | of the grace of tragedy - Steven Weinberg |

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