17 citations · 27 across the 5 of their papers we have counts for
7 papers
On the regularity radius of Delone sets in
Nikolay Dolbilin, Alexey Garber, Undine Leopold +1
We complete the proof of the upper bound for the regularity radius of Delone sets in three-dimensional Euclidean space. Namely, summing up the results obtained ea…
Geometry of simplices in Minkowski spaces
Undine Leopold, Horst Martini
There are many problems and configurations in Euclidean geometry that were never extended to the framework of (normed or) finite dimensional real Banach spaces, although their orig…
Non-existence of polyhedral immersions of triangulated surfaces in
Undine Leopold
We present and apply a method for disproving the existence of polyhedral immersions in of certain triangulations on non-orientable surfaces. In particular, it is pro…
Polyhedral Embeddings and Immersions of Many Triangulated 2-Manifolds with Few Vertices
Ulrich Brehm, Undine Leopold
This article presents an improvement and extension of the heuristic first presented by Hougardy, Lutz, and Zelke in 2010 for realizing triangulated orientable surfaces with few ver…
Monge points, Euler lines, and Feuerbach spheres in Minkowski spaces
Undine Leopold, Horst Martini
It is surprising, but an established fact that the field of Elementary Geometry referring to normed spaces (= Minkowski spaces) is not a systematically developed discipline. There…
Combinatorics and complexity of guarding polygons with edge and point 2-transmitters
Sarah Cannon, Thomas G. Fai, Justin Iwerks +2
We consider a generalization of the classical Art Gallery Problem, where instead of a light source, the guards, called -transmitters, model a wireless device with a signal that…
Vertex-Transitive Polyhedra of Higher Genus, I
Undine Leopold
Since Gruenbaum and Shephard's investigation of self-intersection-free polyhedra with positive genus and vertex-transitive symmetry in 1984 the question of complete classification…