The Nine Gardens Of Eden

Question

_{This puzzle is part of the Monthly Topic Challenge #11: Now in 3D.}

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There are nine distinct known three-cell Garden of Eden patterns in the Life Without Death cellular automata, including the two well-known triominoes. The nine pieces are as follows:

* . *
. . .
* . .

* * .
. . .
* . .

* * .
. . .
. . *

* . .
. . *
* . .

* . .
. . *
. * .

. * .
* . *

* . .
. * *

* .
* *

* * *

Note that some of these pieces are disconnected, but you can't dismantle them. The cells inside each piece must retain their relative positions.

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The task is, can these nine pieces (treated as 1-cell high prisms) be fit perfectly into a 3x3x3 cube?

Answer 1

Is it possible?

Yes!

Labelling the Gardens of Eden for reference:

 R . R
 . . .
 R . .

 S S .
 . . .
 S . .

 T T .
 . . .
 . . T

 U . .
 . . U
 U . .

 V . .
 . . V
 . V .

 . W .
 W . W

 X . .
 . X X

 Y .
 Y Y

 Z Z Z

The following packing works:

 W V W    R W R    S S U
 T Y V    Z Z Z    U T T
 V Y X    R Y X    S X U

This was pretty much all manual trial and error. A trivial checkerboard colouring has the R and W patterns both mono-coloured (everything else is 2:1 or 1:2), so I tried keeping them on opposite colours for balance, which fairly quickly lead to the above solution. I suspect there are others.