This research investigates the application of Triple periodic continuous minimal surfaces in the design of shell structures. It presents different formal outcomes derived from the implementation of a computational algorithm which generates Minimal surfaces having a Quadri-rectangular Tetrahedron as a kaleidoscopic cell, as well as derived from the inclusion of those preliminary results into a parametric system.
In the first stage of research, three different precedents of Triple periodic continuous minimal surfaces are given: a preliminary analysis of Infinite periodical minimal surfaces without self-intersections by Allan H. Shoen followed by an example of the partitioning of three-dimensional Euclidian space into Rheotomic Surfaces by Daniel Piker, and finally an investigation of Betting Kelvin´s partition of space from 14-sided polyhedrons, that later is used by Ken Brakke as a kaleidoscopic cell for the generation of minimal surfaces that belongs to the Batwing family.
In the second stage, different shell morphologies are tested in the parametric system. Distinct formal outcomes are selected according to possible shell structures. Through use of this parametric algorithm and relevant methods, a total of five shell typologies are developed and presented, all of them are based on triple periodic minimal Surfaces from the Batwing family, and finally designed according to the specific program, environment and semiotics.