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Original scientific paper

Orthologic Tetrahedra with Intersecting Edges

Hans-Peter Schröcker   ORCID icon ; University of Innsbruck, Innsbruck, Austria

Fulltext: english, pdf (378 KB) pages 13-18 downloads: 658* cite
APA 6th Edition
Schröcker, H. (2009). Orthologic Tetrahedra with Intersecting Edges. KoG, 13. (13.), 13-18. Retrieved from
MLA 8th Edition
Schröcker, Hans-Peter. "Orthologic Tetrahedra with Intersecting Edges." KoG, vol. 13., no. 13., 2009, pp. 13-18. Accessed 22 Feb. 2020.
Chicago 17th Edition
Schröcker, Hans-Peter. "Orthologic Tetrahedra with Intersecting Edges." KoG 13., no. 13. (2009): 13-18.
Schröcker, H. (2009). 'Orthologic Tetrahedra with Intersecting Edges', KoG, 13.(13.), pp. 13-18. Available at: (Accessed 22 February 2020)
Schröcker H. Orthologic Tetrahedra with Intersecting Edges. KoG [Internet]. 2009 [cited 2020 February 22];13.(13.):13-18. Available from:
H. Schröcker, "Orthologic Tetrahedra with Intersecting Edges", KoG, vol.13., no. 13., pp. 13-18, 2009. [Online]. Available: [Accessed: 22 February 2020]

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.

orthologic tetrahedra; orthosecting tetrahedra; isogonal conjugate

Hrčak ID: 47618



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