What does Ra mean with the other mind, mass mind and infinite mind?

[Sacred Fool]

I can understand it  a bit but I have no idea what geometry and geography have to do with that.

Good question.

I may come off as a cranky old fart when I say this, but when you begin your inquiry asking about step five instead of step one--apparently thinking nothing of leaping over the supporting material to stand atop the apex--I'm reminded of countless others who have traveled here before you who went the same way (with various other topics) and never found much satisfaction, so far as I could see.  In other words, it's probably easier to grapple with the same concept at the earlier stage when matters are more simple.  To wit:

Within the door lies an hierarchical construction you may liken unto geography and in some ways geometry, for the hierarchy is quite regular, bearing inner relationships.

Begin by cracking open the door of your own mental space.  In other words, learn to be observant, poised and composed rather than distracted and antsy.

Next, observe the details of how your mind organizes its mentation (and, thus, your attention and your conception of your experience).  For instance, the material points to the constant play of opposing impulses or forces.  I.e., the mind organizes information/experience in relation to opposing features: up-down, good-bad, etc. instead of some alternative relationship.  Perhaps right now you're thinking, yeah one part of that is right, but another part is wrong?  It's no big deal, the point is just to understand the process from the inside, if you will, to see how your mind informs you of your experience. 

And what you will find, because of this manner of understanding (via opposites) will be highly fragmented.  The ups may be stored over here while a bunch of the downs are located two flights below.  So, the instruction is to internally unify the sense of opposites so that your mental instrument becomes far more poised and balanced within itself.  Eventually, it is implied that through this process you will find a far greater sense of completeness within that thing called you.

To finally move towards your question, you may find that there are repeating patterns in this game--on the personal level, the person-to-person level, the social level--where ways of grasping and organizing information/experience are repeated at these various levels.  My guess is that Ra was thinking of these repeating patterns of thought processing on various levels as being like a geometric pattern, say, where smaller triangles add up to form larger triangles or where aspects of the morphology of one area are recapitulated over in a different area.  I think they were just trying to be picturesque....in a potentially confusing sort of way.  I certainly thought the same thing ("huh?") when I first read that passage.  That particular choice of "decoration" can have the effect of obscuring the relative simplicity of the general intended message, in my view.  But, you know, for a group of far out space aliens, they do an okay job with respect to clarity much of the time.  I don't claim for myself any higher standard of performance, to be honest.