## 172 Citations

A ug 2 01 4 New Lower Bound for the Optimal Ball Packing Density of Hyperbolic 4-space ∗

- 2018

In this paper we consider ball packings in 4-dimensional hyperbolic space. We show that it is possible to exceed the conjectured 4-dimensional realizable packing density upper bound due to L.…

Horoball packings related to the 4-dimensional hyperbolic 24 cell honeycomb {3,4,3,4}

- Mathematics
- 2018

In this paper we study the horoball packings related to the hyperbolic 24 cell honeycomb by Coxeter-Schläfli symbol {3, 4, 3, 4} in the extended hyperbolic 4-spaceH where we allow horoballs in…

Upper bound of density for packing of congruent hyperballs in hyperbolic $3-$space

- Mathematics
- 2018

In \cite{Sz17-2} we proved that to each saturated congruent hyperball packing exists a decomposition of $3$-dimensional hyperbolic space $\mathbb{H}^3$ into truncated tetrahedra. Therefore, in order…

New Lower Bound for the Optimal Ball Packing Density in Hyperbolic 4-Space

- Mathematics, Computer ScienceDiscret. Comput. Geom.
- 2015

It is shown that it is possible to exceed the conjectured 4-dimensional realizable packing density upper bound due to L. Fejes-Tóth (Regular Figures, Macmillian, New York, 1964).

Tessellations of hyperbolic surfaces

- Mathematics
- 2011

A finite subset S of a closed hyperbolic surface F canonically determines a "centered dual decomposition" of F: a cell structure with vertex set S, geodesic edges, and 2-cells that are unions of the…

Coverings with horo- and hyperballs generated by simply truncated orthoschmes

- MathematicsNovi Sad Journal of Mathematics
- 2021

After having investigated the packings derived by horo- and hyperballs related to simple frustum Coxeter orthoscheme tilings we consider the corresponding covering problems (briefly hyp-hor…

The ratio of homology rank to hyperbolic volume, I

- Mathematics
- 2021

We show that for every finite-volume hyperbolic 3-manifold M and every prime p we have dimH1(M ;Fp) < 168.05 · volM . This improves on a result proved by Agol, Leininger and Margalit giving the same…

Five Essays on the Geometry of László Fejes Tóth

- Mathematics
- 2018

In this paper we consider the following topics related to results of Laszlo Fejes Toth: (1) The Tammes problem and Fejes Toth’s bound on circle packings; (2) Fejes Toth’s problem on maximizing the…

Geometries of Hyperbolic Surfaces with and without Boundary

- Mathematics
- 2018

In this dissertation, I will investigate three different points of view of maximizing packings on complete hyperbolic surfaces with finite area, possibly with geodesic boundary. This optimization…

## References

SHOWING 1-10 OF 10 REFERENCES

The Closest Packing of Spherical Caps in n Dimensions

- Mathematics
- 1955

Let S n denote the “surface” of an n -dimensional unit sphere in Euclidean space of n dimensions. We may suppose that the sphere is centred at the origin of coordinates O , so that the points P ( x…