Neshomeh was right, it's the Playscriptes. Specifically the second one, and even more specifically, scene 3:

~~~~~~~

Daisy: Let's see. You know about the three so-called 'physical' dimensions, yes?
Alex: Up and down, side to side, and back and forth, yes. And the fourth one is time. But what about the other two?
Daisy: Very good. The other two, then, are probability and consciousness.
Alex: But that can't be right. You can't move in consciousness, or probability for that matter. [Pause] Can you?
Daisy: Agent Orange, you move in probability every time you go into an alternate fic-verse. And, to a lesser extent, every time you use a portal. It's the difference between the probability of you being at one end over the other, and the ability to change those probabilities, that make them work.
Alex: Portals change probabilities? But they can't do that without changing the laws of physics. If they try, they make a-
Daisy: Plothole, yes. Not many people know this, but portals were originally made from plotholes. In fact, as I've just explained, they still are.
Alex: [Nods slowly] All right. Probability, yes. But what about consciousness?
Daisy: Alex, you already know about this one. How do you get between places in HQ as fast as possible?
Alex: You don't pay attention to the route. Everyone knows... oh. Oh
Daisy: Exactly. A move 'backwards' in consciousness, that is, a move towards the unconscious, tends to make the route shorter. I say tends to, as there are some places, such as where you first met me, where it is still necessary to be on the right floor.

~~~~~~~~~~~~

So, 1 (left-right), 2 (up-down), 3 (in-out), 4 (time), 5 (probability), 6 (consciousness). They proceed to use carefully tuned alcohol to get around quickly.

Of course, it's possible HQ has more dimensions - but 6 is all the Flowers can see. (And no, I don't /think/ they can see time directly - but time's always the odd one out).

hS

Headquarters exists in six dimensions. The world that humans can see and move around in is in three directions. You know, 3d.

HEY YOU GUYS. SLIGHT SPECULATION TIME. LET ME KNOW IF THIS SOUNDS ABOUT RIGHT:

It's very hard to imagine, but think of it this way: Somebody tells you to move in a direction that is not forward, back, sideways, up, or down. You can't actually do that-- that's the three dimensional world we live in. But the Flowers can move in those other directions at will, and see in them too. Headquarters is also built in those other directions that most people can't see or comprehend.

Really, part of the reason why Headquarters is hard to navigate is because humans (and others) in HQ may be moving in those other directions in any given time and not know it. So when you think you're turning left, you may actually be turning something you think is left, but is really not left, right, up, down, sideways, forwards or back. The not-left direction may look and seem left to you, but it's not. It's a totally different way.

Hence the wrong turns and how paying attention while walking gets you nowhere. If you can't even comprehend the direction you're supposed to go, sometimes just not caring where you go can allow you to take that path that you don't even know is there...

It's six dimensional, but that's a whole other story. And what it means is that it's really, really, really hard to find your way around.