# Filaments of galaxies and Voronoi diagrams

## TL;DR

This paper explores the distribution of galaxy clusters by analyzing intersections of Voronoi polyhedrons with spherical shells, linking geometric structures to cosmological models and galaxy clustering.

## Contribution

It introduces a method to identify galaxy cluster nodes via Voronoi diagram intersections within a cosmological context.

## Key findings

- Nodes correspond to potential galaxy clusters.
- Method aligns with LCDM cosmology predictions.
- Provides a geometric approach to galaxy distribution analysis.

## Abstract

The intersections between a spherical shell and the faces of Voronoi's polyhedrons are numerically evaluated. The nodes of these intersections are the points that share the same distances from three nuclei. The nodes are assumed to be the places where we will find clusters of galaxies. The cosmological environment is given by the coupling between the number of galaxies as function of the redshift and the LCDM cosmology.