Modeling the Gyroid in GeoGebra

Abstract

The gyroid is a triply periodic minimal surface (TPMS) with intriguing geometric and aesthetic appeal. However, it is a challenging structure to model in GeoGebra. Starting with the $G*$ implicit equation, we first derive a parametric equation to model the gyroid unit surface patch in light of its intrinsic symmetries. Next, we demonstrate how JavaScript codes and GeoGebra Sequences can be employed to create 3D scatterplots of the gyroid unit cell. Through this process, we showcase the interplay between GeoGebra's capabilities, its limitations, and the computational complexity involved in gyroid modeling.