Revisiting an unravelling

This is based on an old pattern where I took a clockwise loop of 6 pentagons and combined them with two counter clockwise loops of 3 hexagons resulting in a clockwise loop of pentagons and hexagons. One way to think about the process is to imagine unravelling the loop of pentagons. I used this pattern back in back in 2007 and 2006 but this one has a bit more of a twist.
Perhaps I should come up with a visual of this unravelling. I was hoping I would find one in my blog but I didn't. I should make a better index for this thing...done. In this screen capture, you can see that the outside of the original pentagon loop is now the inside of the composed shape and the inside of the original loop corresponds to the 4 sides of the pentagons the are on the outside of the composed shape. Perhaps I'll play some more with this ‡(double dagger shape which I found its html code here).