TL;DR
This paper constructs a 6-regular geodesic triangulation of the hyperbolic plane, expanding the understanding of regular triangulations across different geometries.
Contribution
It introduces the first known 6-regular geodesic triangulation of the hyperbolic plane, filling a gap in geometric triangulation theory.
Findings
Established a 6-regular geodesic triangulation for the hyperbolic plane.
Extended the class of regular geodesic triangulations to include this new case.
Provides a geometric construction method for the triangulation.
Abstract
It is well-known that the Euclidean plane has a standard 6-regular geodesic triangulation , and the unit sphere has a 5-regular geodesic triangulation, which is induced from the regular Dodecahedron, and the hyperbolic plane has an n-regular geodesic triangulation for any n > 6. Here we constructed a 6-regular geodesic triangulation of the hyperbolic plane.
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Taxonomy
TopicsMathematics and Applications · Computational Geometry and Mesh Generation · Graph Labeling and Dimension Problems