This volume collects papers based on talks given at the conference "Geometrias'19: Polyhedra and Beyond", held in the Faculty of Sciences of the University of Porto between September 5-7, 2019 in Portugal. These papers explore the conference's theme from an interdisciplinary standpoint, all the while emphasizing the relevance of polyhedral geometry in contemporary academic research and professional practice. They also investigate how this topic connects to mathematics, art, architecture, computer science, and the science of representation. Polyhedra and Beyond will help inspire scholars, researchers, professionals, and students of any of these disciplines to develop a more thorough understanding of polyhedra.

Autorentext

Vera Viana is a Researcher in the Faculty of Architecture, University of Porto specialized on geometry, polyhedral theory, history of polyhedra, the relationships between architecture and mathematics, and the enhancement of mathematics education in higher education through advanced digital tools.

Inhalt

Synthetic Methods for Constructing Polyhedra.- Sources and Features of the Small Stellated Dodecahedrons Painted in Genoa.- Polyhedral Transformation Based on Confocal Quadratic Surface Properties. Graphical Speculations.- Concave Deltahedral Rings based on the Geometry of the Concave Antiprisms of the Second Sort.- Filling Space with Gyroid Symmetry.- Odd Or Even, Jitterbug Versus Grünbaum's Double Polyhedra.- From Geometry to Reality: Designing Geodesic Structures.- Vittorio Giorgini's Architectural Experimentations at the Dawn of Parametric Modelling.- Architectural Inversions: The Intangible Aspect as a Form-Finding Factor in the Combined Work of Antoni Gaudí and John Pickering.- An Introduction to Solid Tessellations with Students of Architecture.