Hello, you can refer the book "Response Surface Methodology" by Khuri. Regarding the rotatability of any design is related to the prediction variance of any design (), where X is the design matrix. Now for a rotatable design the prediction variance must be same at every points which are at the same distance from the center of the design. The advantage of this property is that the prediction variance remains unchanged under any rotation of the coordinate axes.

Sorry the equation I wrote here is not coming proper.

Hi, you can refer to the review paper wrote by Andre´ I. Khuri∗ and Siuli Mukhopadhyay. Please refer to the attachment.