Imaginary Cube

Imaginary Cube Puzzle 3H=6T
Solution

We show one solution without gaps between pieces.
This is the unique solution without gaps modulo rotation of the box.

1.
First put a H.
We place it so that it makes space at the center of the box.

2.
Place T next to it.
Arrange it so that it touches H with the same isosceles traiangle face as H has.

3.
Place another T also on the other side.

4.
Put another T in the last space on the lower side.
This time, the T touches two other T pieces with edges of the big regular triangle.

There is a hollow in the center.
It exactly has the shape of sharp vertex of T.

5.
Place a T at the center.

6.
Put pieces on the upper side so that pieces tough through faces with the same shape.

7.


8.


9.
Complete.


This (and its rotations) are the only solution of the puzzle without gaps between pieces. There are many other ways to put nine pieces if we allow gaps between pieces.