What are invoking and banishing pentacles? Are they used often? Do you use them? And do I have the interpretation of the diagram correct?
I am currently at work, and the book is at home, but I can mostly help with this one anyway.
Invoking and banishing pentagrams are (at least as I was taught) how you open up doorways between your circle (closed sphere) and the realms of the elemental guardians/elementals/elemental powers. Basically, it is intended to be a very focused tunnel through your circle to a specific location.
The confusing thing for a lot of people is that there's several different versions of the pentagrams going around. Some people just use invoking and banishing of earth for everything (banishing earth is usually the way many people naturally draw five pointed stars: start at the bottom left point, top, bottom right, left, right, bottom left.)
Other people use different invoking and banishing pentagrams for each quarter, but exactly how - well, there's several variations. My basic take is "Figure out which one works into your larger structure, and go with that."
I've done both my trad's version, and a version which starts in the same places, but then goes so the open angle is always opening clockwise for invoking, and opening counter clockwise for banishing - which also works, but produces somewhat different energetic results (even when we're using the same words/visualisation for the rest of the quarter call.)
So, if you're doing earth, which is a little easier because it's one of the bottom points:
The earth point is often considered to be the bottom left. In the trad system, to invoke, you start at the line before the elemental point, travel to it, and then go from there - so you'd start at the top point, bottom left, right, left, bottom right, top.
To banish, you start at the point, and move away, so bottom left, center, bottom right, left, right, bottom left.
I like the diagram here:
http://tarotconnection.net/episode-52/ which is about as clear a version as I've seen. Note that you do not have direct lines of connection between the two theoretically opposing elements (fire and water, and to a lesser extent earth and air.) and you do have direct connection lines between the traditionally 'active' elements (air, fire) and 'receptive' ones (earth, water) which is a good way to keep track of which one goes where.
If I were playing with the open angle version, I'd start (for earth) at the bottom left, then the open angle turning right is to the top center, then bottom right, then left, then right, then bottom left. That'd be invoking (which is banishing for everyone else's theory). For banishing, start at bottom left again, but move to the right point, left, bottom right, center, bottom left. It's weird, but like I said, seemed to work - just with different energy flows.
Using the traditional ones does tie into the weight and memory all of the other uses, across time, of that pattern - which can be a really handy thing. But directed intention can also matter for a whole lot.