Axial collineation

Abstract

We can characterize collineation with an imaginary involution by two such self-collinear rays, of which one is infinitely distant in the horizontal plane, and the other is vertical. Although these two rays are truly self-collinear, and in no way are the axes of collineation with a real involution, but as two special ray, characterizing the symmetries of the system, we could conditionally call them the axes of imaginary collineation (conventional abbreviation of collineation with imaginary involution). We see that these systems have a center, three double axes of symmetry passing through it, and three planes of symmetry passing in pairs through the two axes of symmetry.