Original scientific paper

Orthologic Tetrahedra with Intersecting Edges

Hans-Peter Schröcker orcid.org/0000-0003-2601-6695 ; University of Innsbruck, Innsbruck, Austria

Abstract

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.

Keywords

orthologic tetrahedra; orthosecting tetrahedra; isogonal conjugate

Hrčak ID:

47618

URI

https://hrcak.srce.hr/47618

Publication date:

25.1.2010.

Article data in other languages: croatian

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