Let F = {1 + εr : r ∈ H }, ε = 0. Note that F is stable under the rotation q → p qp and under the translation (1 + εr)(1 + εs) = 1 + ε (r + s) for any vector quaternions r and s. F is a 3-flat in the eight-dimensional space of dual quaternions. This 3-flat F represents space, and the homography constructed, restricted to F, is a screw displacement of space.