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math.MG2026
The two most symmetric flat tori as eight-vertex paper tori
Fabian Lander
A paper torus is a polyhedral torus embedded in whose intrinsic metric is locally Euclidean, a torus folded from a flat sheet of paper. Many constructions are known,…
math.HO2026
Illustrating Hyperbolic Surfaces with Mesh Embeddings
Fabian Lander, Erik Löffelholtz, Diaaeldin Taha +2
Hyperbolic geometry exhibits geometric phenomena, such as fast area growth, that are difficult to visualize faithfully in Euclidean space, and which standard models like the Poinca…
math.DS2026
Symplectic Tiling Billiards on Complete Affine Tori
Charles Daly, Fabian Lander
In 2023, Richard Schwartz introduced a new dynamical system which is a marriage of two types of familiar billiards, tiling billiards and symplectic billiards. In this paper we inve…