A desirable property of a response surface design, in which any two points that are the same distance from the design center, have the same prediction variance. A design which exhibits this property is said to be 'rotatable'.
Rotatability ensures equal precision of the predictions at points that are the same distance from the center point in any direction. Because the region of optimum response is not known at the start of the experiment, this property provides a ‘level playing field’ so that there is no bias in the estimates of predicted points no matter what direction the invetigation takes.
In a Contour Plot of prediction variance, this design is characterized by concentric circles. All points falling on a particular circle/contour can be estimated with the same magnitude of error.
Response Surface Designs and rotatability from NIST: - http://www.itl.nist.gov/div898/handbook/pri/section3/pri336.htm