Discrete minimal nets with symmetries

TL;DR

This paper extends the Schwarz reflection principle to discrete minimal surfaces, enabling the construction of highly symmetric discrete minimal nets with potential applications in geometric modeling.

Contribution

It introduces a discrete analog of the Schwarz reflection principle for minimal surfaces and uses it to generate symmetric discrete minimal nets.

Findings

Developed a discrete Schwarz reflection principle

Constructed new symmetric discrete minimal nets

Enhanced understanding of discrete minimal surface symmetries

Abstract

In this paper, we extend the notion of Schwarz reflection principle for smooth minimal surfaces to the discrete analogues for minimal surfaces, and use it to create global examples of discrete minimal nets with high degree of symmetry.