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Orthologic Tetrahedra with Intersecting Edges

Hans-Peter Schröcker orcid id ; University of Innsbruck, Innsbruck, Austria

Puni tekst: engleski pdf 378 Kb

str. 13-18

preuzimanja: 975



Two tetrahedra are called orthologic if the lines through vertices of one and perpendicular to corresponding faces of the other are intersecting. This is equivalent to the orthogonality of non-corresponding edges. We prove that the additional assumption of intersecting non-corresponding edges (“orthosecting tetrahedra”) implies that the six intersection points lie on a sphere. To a given tetrahedron there exists generally a one-parametric family of orthosecting tetrahedra. The orthographic projection of the locus of
one vertex onto the corresponding face plane of the given tetrahedron is a curve which remains fixed under isogonal conjugation. This allows the construction of pairs of conjugate orthosecting tetrahedra to a given tetrahedron.

Ključne riječi

orthologic tetrahedra, orthosecting tetrahedra, isogonal conjugate

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