Axial collineation

Abstract

A collineation with an imaginary involution can also be characterized 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 indeed self-collinear, and are in no way axes of collineation with a real involution, as two special rays, characterizing the symmetry of the system, we could conditionally call them the axes of imaginary collineation (a conventional abbreviation for collineation with an imaginary involution). We see that these systems possess a center, three double axes of symmetry passing through it, and three planes of symmetry, each passing through a pair of these axes.

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