Once I brought this shape into 123D Make and fiddled with the options they give you, I was able to land on a slicing technique and angle that I really liked. I also kept an eye out for floating small parts that would break easily. After about an hour or so of playing around, I was satisfied.
The program gives you a spot for you to put in the thickness of your material, which also changes the look of your design. You'll want to take this into account when doing your own version.
Since Paul had plenty of acrylic laying around his studio, we decided that before going big, we would first do up a quick prototype using some acrylic. We scaled the model down by 1/3 until it was 12" in diameter and went with a material thickness of 1/8" since we had more of this in kicking around.
On the right hand side of the screen, 123D Make displays the lines that are used to cut out the shape of each slice in whatever material it is you choose to use. Keep an eye out for little pieces that might break when cutting or moving around and adjust your number of slices and/or angles to find the best outcome you can.
We hit the 'Get Plans' button and save the outlines of the slices. I chose to use an EPS extension since I knew this would easily import into Corel Draw. Unfortunately, 123D Make doesn't do so well at saving cut material by 'nesting' the parts tight into one another. I was able to do this in Corel Draw by hand but this took some time in order to reduce the number of 18"x24" sheets I had to use. Regardless of that, it's all worth it. Not nesting your parts is wasteful and shame on you if you don't do this.