Henry Ernest Dudeney/Modern Puzzles/146 - The Cardboard Box/Solution

Modern Puzzles by Henry Ernest Dudeney: $146$

If I have a closed cubical cardboard box, by running the penknife along seven of the twelve edges (it must always be seven)

I can lay it out in one flat piece in various shapes.

Thus, in the diagram, if I pass the knife along the darkened edges and down the invisible edge indicated by the dotted line, I get the shape $A$.

Another way of cutting produces $B$ or $C$.

It will be seen that $D$ is simply $C$ turned over, so we will not call that a different shape.

Now, how many shapes can be produced?

The $11$ basic shapes are:

All of these are asymmetrical except the first $2$ shapes.

Hence another $9$ can be flipped over to make a different shape.

So there are $20$ altogether.