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Open AccessArticle

The Existence of a Convex Polyhedron with Respect to the Constrained Vertex Norms

1
Advanced Research Center for Computational Simulation, Department of Mathematics, Faculty of Science, Chiang Mai University, 239 Huaykaew Road, Suthep District, Muang, Chiang Mai 50200, Thailand
2
Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japan
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 645; https://doi.org/10.3390/math8040645
Received: 30 March 2020 / Revised: 14 April 2020 / Accepted: 18 April 2020 / Published: 22 April 2020
(This article belongs to the Special Issue Modern Geometric Modeling: Theory and Applications)
Given a set of constrained vertex norms, we proved the existence of a convex configuration with respect to the set of distinct constrained vertex norms in the two-dimensional case when the constrained vertex norms are distinct or repeated for, at most, four points. However, we proved that there always exists a convex configuration in the three-dimensional case. In the application, we can imply the existence of the non-empty spherical Laguerre Voronoi diagram. View Full-Text
Keywords: convex polyhedron; convex configuration; spherical Laguerre Voronoi diagram convex polyhedron; convex configuration; spherical Laguerre Voronoi diagram
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Chaidee, S.; Sugihara, K. The Existence of a Convex Polyhedron with Respect to the Constrained Vertex Norms. Mathematics 2020, 8, 645.

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