Mixtures and grain boundaries of P, D, and G triply periodic minimal surfaces

TL;DR

This paper introduces a novel square tiling representation for P, D, and G triply periodic minimal surfaces, facilitating the identification of mixtures and grain boundaries relevant to material science and manufacturing.

Contribution

It presents a new tiling-based method for analyzing triply periodic minimal surfaces and explores generalizations to complex topologies and other tilings.

Findings

Effective identification of mixtures and grain boundaries.

Applicability to advanced material design.

Extension to complex tiling topologies.

Abstract

We introduce a square tiling/tetragonal strip representation to the P, D, and G triply periodic minimal surfaces. This approach is useful in identifying mixtures and grain boundaries of these surfaces that might be useful for material sciences or advanced manufacturing purposes. Generalizations to more complicated strip topology (multi-strand) as well as other regular and semi-regular tilings are discussed. Examples of these include double diamond, double gyroid, and triangular P/D/G surfaces.