We consider the geometry of four spatial displacements, arranged in cyclic
order, such that the relative motion between neighbouring displacements is a
pure rotation. We compute the locus of points whose homologous images lie on a
circle, the locus of oriented planes whose homologous images are tangent to a
cone of revolution, and the locus of oriented lines whose homologous images
form a skew quadrilateral on a hyperboloid of revolution
