# Imaginary Cube

## Imaginary Cube Puzzle 3H=6T

The objective of this puzzle is to put nine pieces into a cubic box.

The pieces are two imaginary cubes H and T, and this puzzle is based on beautiful geometries of these polyhedrons. Have a lot of fun solving the puzzle, and read the mathematical backgrounds they have, if you are interested in it.

### Pieces:  Hexagonal Bipyramid Imaginary Cube (H, in short) is obtained by glueing two hexagonal pyramids on their bottoms.  Triangular Antiprismoid Imaginary Cube (T, in short) is obtained by truncating three vertices of a triangular prism.

### Exercise: The above H and T fits into cubic box with side length one. Can you imagine it?

### Solution:  H fits into a box in this way.  T fits into a box in this way.
They look square from each face of the cube. This kind of objects are called imaginary cubes.

### The Puzzle: Put three H and six T into this double-sized box. Since H and T fit into small boxes, it is easy to put 8 pieces. Here, you have nine.
How can you put all of them?