How many vitrified doors are there in Portal 2?

I'm trying to get the Door Prize achievement in Portal 2, by investigating vitrified doors. I don't want spoilers to their locations or areas, but I would appreciate knowing

• How many vitrified doors are there?

• In how many different areas do I need to look?

Here is what I've achieved so far:

In the entrance to the Aperture Science Innovators area there are three vitrified doors, one of which is smashed open and provides access to the rest of the area. None have special properties.

Near the top of the same area, before entering the pumping station, there are three more vitrified doors. Each one has a small panel with a button you can press, after which Cave Johnson says something.

I give this detail in case I've found all the doors but have somehow failed to "investigate" them properly.

Additional information:

The first group of three vitrified doors is in Chapter 6, relatively soon after someone has spoken to you.
I have it on good authority that the second group of vitrified doors is also in Chapter 6.

In order to get credit for each door, you must activate a little box with an intercom which start a short humorous announcement from Cave Johnson. There are a total of six of these "intercom" things. If the door you are looking at doesn't have a working intercom thing, it doesn't count towards the achievement - keep looking. A good video guide is here if you decide you want more detail.