Imaginary Cube

Imaginary Cube Puzzle 3H=6T
Clues


Clue1:

You can put 8 pieces as if they are in small boxes.
Where does the 9th piece fit in?

Clue 2:

Gather the trancated vertex at the center of the cube to make a space.
Which piece comes at the center? H or T?

Clue 3:

One can fit 9 pieces so that there is no gap between pieces.
In such a solution, faces of the same shape will touch each other.

Clue 4:

Place one piece so that it leaves a space at the center of the box.
Put a piece so that it touches the piece with the same face.
Continue...