When exploring response surfaces in spherical regions. rotatable designs possess the property that the estimated response has a constant variance at points which are equidistant from the center of the design, in other words, the precision is constant on spheres. In three-component or ternary mixture systems where the experimental region is an equilateral triangle, it would be desirable to have the predicted response possess constant variance on each triangle of a set of concentric interior triangles. This paper presents a mapping function which maps two-dimensional concentric circles onto concentric equilateral triangles. The property of a constant variance on the circle in a family of concentric circles is preserved under the mapping resulting in the variance being constant on the equilateral triangle onto which the circle is mapped. The method is illustrated using data from a three-component sensory testing experiment and the extension to higher dimensional cases is outlined briefly.