# Identifying method by equation (Related to Factorial Fractional Design)

I'd like to know the name of the method in the picture below. It's the same category as full - and factorial fractional design. It's quite difficult to search the net for this equation - I've tried wolfram etc but to no avail. If I remember correctly it's a response design of some kind(?) but I might be wrong.

Thanks for your help. I've read up on central composite design but I'm not sure if I understand it completely.

So I've my variables x1,x2,x3 represented as a cube and I add the center point to see if the variables are linear - what if they are not? Then I add the star points from the center point to see what variable affect the response the most. Is this an accurate description of the essence of the methodology or have I misunderstood/missed something?

Is the number of "experiments" or runs I need to do >= 9? Because 2³ (yellow dots) + 1 center point are 9 runs? I'm trying to compare central composite design with full fractional design (2³=8 runs) and fractional factorial design (with 1/2 fraction: 4 runs).