# Pentomino - is there any solution with the straight-bar piece in the middle of a rectangle?

Is there a solution for a straight-bar piece not touching the edge of the rectangle? By rectangle solution, I mean either one of the patterns 15x4, 12x5, or 10x6. By straight-bar piece, I mean the piece of 5 stones in a straight row. Literate pentomino crackers denote this piece with the letter "I".

Here's one solution for the $$10{\times}6$$ rectangle:

Here are all $$11$$:

vvvllllzzy
viiiiilzyy
vxffwwzzny
xxxffwwtny
uxufppwtnn
uuuppptttn

vvvllllzzn
viiiiilznn
vxffwwzzny
xxxffwwtny
uxufppwtyy
uuupppttty

yzzllllvvv
yyzliiiiiv
ynzzwwxffv
yntwwxxxff
nntwppxufu
ntttpppuuu

nzzllllvvv
nnzliiiiiv
ynzzwwxffv
yntwwxxxff
yytwppxufu
ytttpppuuu

tnnnllllpp
tttnnfflpp
tiiiiiffxp
vvvzwwfxxx
vzzzywwuxu
vzyyyywuuu

wwtttxffuu
pwwtxxxffu
ppwtyxzfuu
ppyyyyzzzv
liiiiinnzv
llllnnnvvv

pptttxffuu
ppwtxxxffu
pwwtyxzfuu
wwyyyyzzzv
liiiiinnzv
llllnnnvvv

wwfftttxuu
pwwfftxxxu
ppwfytzxuu
ppyyyyzzzv
liiiiinnzv
llllnnnvvv

ppfftttxuu
ppwfftxxxu
pwwfytzxuu
wwyyyyzzzv
liiiiinnzv
llllnnnvvv

uuxfftttpp
uxxxfftwpp
uuxzfytwwp
vzzzyyyyww
vznniiiiil
vvvnnnllll

uuxfftttww
uxxxfftwwp
uuxzfytwpp
vzzzyyyypp
vznniiiiil
vvvnnnllll


There is only one solution for the $$12{\times}5$$ rectangle:

There are no solutions for the $$15{\times}4$$ rectangle.