Journal for Geometry and Graphics 29 (2025), No. 1, 019--022
Copyright by the authors licensed under CC BY SA 4.0
Sums of Distances from a Point to the Faces of Polyhedra. Generalizations of Viviani’s Theorem
Jens Wittenburg
Institute for Technical Mechanics, Institute of Technology, Karlsruhe, Germany
jens.wittenburg@kit.edu
Kuno Egle
Institute for Technical Mechanics, Institute of Technology, Karlsruhe, Germany
kuno.egle@gmx.de
Theorems of Viviani and Walser, Vargyas on sums of distances from a point to the sides of polygons are generalized for polyhedra in the euclidean n-space (n ≥ 3).
Keywords: Viviani’s theorem, signed distance from a point to lines and planes, polygon, polyhedron, equifacial tetrahedron, insphere radius, Platonic solid, polyhedron in euclidean n-space.
MSC: 51N20; 52B10
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