# Delone lattice studies in C3, the space of three complex variables

## TL;DR

This paper investigates Delone scalars within the space of three complex variables, enhancing understanding of lattice reduction and classification in complex three-dimensional space.

## Contribution

It introduces a study of Delone scalars specifically in ^3, linking them to lattice reduction and type determination in complex three-dimensional space.

## Key findings

- Delone scalars are characterized in ^3
- The structure of complex coordinate planes is elucidated
- Implications for lattice classification are discussed

## Abstract

The Delone (Selling) scalars, which are used in unit cell reduction and in lattice type determination, are studied in $\mathbb{C}^3$, the space of three complex variables. The three complex coordinate planes are composed of the six Delone scalars.