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This is not an answer, but I'd like to point out that the concepts in question are projective, although they have a special Euclidean case. Consider the diagram below. Start with a conic $\gamma$(green), a triangle $ABC$ inscribed in $\gamma$, and a line $\omega$ (black dot-dashed). Let $X$ be the polar of $\omega$ wrt the conic, and draw a line (dotted) ...
An example is given by the canonical class $K_S$ of a bielliptic surface $S$, which is torsion of order $h_0=2, 3, 4$ or $6$. For the definition of a bielliptic surface see for instance Chapter VI of Beauville's book "Complex algebraic surfaces".