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math.MG2021
On Menelaus' and Ceva's theorems in Nil geometry
Jenő Szirmai
In this paper we deal with $\NIL$ geometry, which is one of the homogeneous Thurston 3-geometries. We define the "surface of a geodesic triangle" using generalized Apollonius surfa…
math.MG2021
Optimal ball and horoball packings generated by -dimensional simply truncated Coxeter orthoschemes with parallel faces
Arnasli Yahya, Jenő Szirmai
In this paper we consider the ball and horoball packings belonging to -dimensional Coxeter tilings that are derived by simply truncated orthoschemes with parallel faces. The goa…