==> geometry/pentomino.s <==
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



--
 +-------------------  pete@bignode.equinox.gen.nz  -------------------+
 | 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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