The most important part of rigging this kind of thing is the placement of the anchor points. They all need to be exactly on the edge of a layer. You'd parent in a chain. Layer 1 to layer 2 to layer 3 to layer 4 to create the first group, then layer 5 through 8 and so on for the four groups required to create the basic shape. Then each of the groups would be parented to their own null set at the bottom edge of the contraption. You would then cross tie the rotation values of the nulls with an expression so that a rotation to the left would create a rotation to the right on it's mate. Each of the 4 nulls would be tied to pair of nulls with rotation linked by expression. Then the pair tied to a last null that controlled position.
The theory is this. The master null controls position and rotation of the whole group. The pair of of nulls controlling the bottom edge (call hinge null 1 and hinge null 2, are tied together so that when you rotate 1 the north and south sections open and when you rotate hinge 2 the east and west sections open. If the hinges are all correctly tied together you can then make this thing do exactly what you want it to do by simply adjusting the rotation of the two hinge nulls. Expression Controls could be added to the master null that control the rotation of these two north/south and ease/west nulls.
As far as laying this thing out here's what I'd do. I'd fold up a piece of paper to create a real decision maker. Then I'd take a pencil and mark each visible side and mark the folds. Then I'd unfold it, take a photo, import the photo into AE and use that photo to layout the thing flat in AE first. Then I'd do the parenting. Then I'd rotate the pieces into place. If you line up the Anchor Points and pay attention to the edges it shouldn't take long to rig the device. If it were me I'd budget an hour.
Wow, thanks Rick.
This is kind of what I'm trying to do now, so I'm pleased to hear I'm not too far off. However, I'm an expression noob so I'm trying to do the rotations manually which is obviously holding me back. Can you recomend any good resources for help here?
Take a look at this project. It uses a equilateral triangle shape layer, and expression adjust the shape layer anchor point to the center tip of the triangle, an expression to rotate the duplicates into perfect position, Nulls and parenting to create the hinge points on the base of the triangle, and a controller to open or close the 'flower.' Come to think of it, it also uses an expression to set the colors of the shape layers.
I hope it helps. You should be able to use the same techniques to accurately create your paper decision maker especially if you use an unfolded paper as a template for creating your shapes and defining your hinge points. You should be able to just lay shape layers over the template, set up the anchor points, parenting and nulls at hinge points, and rotate it into position.
Good luck. I'd love to see the project when it's done.