Polar relations of imaginary triangles and tetrahedrons

Abstract

The known properties of gnomonic projections of trigonaloid crystals prompted me about the presence of the relations mentioned in the title, which seemed to me paradoxical. For the case under consideration, the theory of poles and polars unfolds in its usual form: two points are the poles of two polars and, in turn, determine a line — the polar of the intersection point of these polars. To each vertex of a triangle, the opposite side is polar, etc., and in no case is there a point through which its polar passes, as is the case for imaginary conoprimas of projectivity (see the article).

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