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math.GT2022
Hexagonal Geometric Triangulations
Yanwen Luo, Xiaoping Zhu, Tianqi Wu
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 re…
math.GT2022
Spaces of Geodesic Triangulations Are Cells
Yanwen Luo, Zhenghao Rao, Tianqi Wu +1
It has been shown that spaces of geodesic triangulations of closed negatively curved surfaces are contractible. Here we prove that these spaces are homeomorphic to Euclidean spaces…
math.GT2022
The Deformation Space of Delaunay Triangulations of the Sphere
Yanwen Luo, Tianqi Wu, Xiaoping Zhu
In this paper, we determine the topology of the spaces of convex polyhedra inscribed in the unit -sphere and the spaces of strictly Delaunay geodesic triangulations of the unit…