Polyhedra and Beyond: Contributions from Geometrias’19, Porto, Portugal, September 05-07

Foreword
Preface
Acknowledgments
Contents
List of Figures
List of Tables
Contributors
About the Editors
Chapter 1: Synthetic Methods for Constructing Polyhedra
Introduction
The Synthetic Approach for the Constrction of PS and AS
The General Synthetic Method to Construct a Polyhedron
Conclusions
References
Chapter 2: Scientific Sources and Representations of the Small Stellated Dodecahedra Painted in Genoa
The Frescoes of Palazzo Balbi Senarega
The Small Stellated Dodecahedron: Scientific and Iconographic History
The Small Stellated Dodecahedron in the Room of Leda: Geometric Characteristics and Symbolic Meaning
Observations on Shadows
Conclusions
References
Chapter 3: Polyhedral Transformation Based on Confocal Quadratic Surface Properties. Graphical Speculations
Introduction
Generalization of One Property of the Archimedes Paraboloid
Area of Application, Objectives, and Methodology
From Plane to Space. Graphic Methods
The Method of the Flat Polygonal Patterns
The Method of the Circumference Mesh
Discussion. Beyond the Stereographic Projection
From Spheres to Other Quadrics. Projecting by Cones
Projecting by Ellipsoids, Paraboloids, or Hyperboloids
Discussion. Graphical Characterization of 3D Homology
Conclusions
References
Chapter 4: Concave Deltahedral Rings Based on the Geometry of Concave Antiprisms of the Second Sort
Introduction
Investigating a Possibility for the Deltahedral Rings’ Formation
Findings of the Research
Conclusions
References
Chapter 5: Filling Space with Gyroid Symmetry
Minimal Surfaces
Discrete Minimal Surface
The Gyroid Surface
A Discrete Gyroid Surface
Space-Filling Solids
Filling Half-Space
A. H. Schoen’s M6 Surface
Cutting at Smooth Gyroid Surface
Conclusions
References
Chapter 6: Odd or Even, Jitterbug Versus Grünbaum’s Double Polyhedra
Introduction
Jitterbug Transformations Applied to Non-Convex Polyhedra
Face-Doubling
Jitterbug Transformation Applied to Infinite Uniform Polyhedra
Conclusion
References
Chapter 7: From Geometry to Reality: Designing Geodesic Structures
Introduction
The Subdivision Methods
Study Case: The GoodKarma Constructive Method
Comparing the Results
Conclusions
References
Chapter 8: Vittorio Giorgini’s Architectural Experimentations at the Dawn of Parametric Modelling
Introduction
Giorgini as a Morphologist-Spatiologist Architect
Giorgini as a Pioneer of Parametric Design
Giorgini Parameterized
Conclusions
References
Chapter 9: Architectural Inversions: The Intangible Aspect as a Form-Finding Factor in the Combined Work of Antoni Gaudí and John Pickering
Introduction
Design Process in Gaudí’s Later Years: 1914–1926
Ruled Surfaces in Design: Hypar & Hyperboloid of Revolution of One Sheet
Complexity in the Sagrada Familia: Computational Thinking & Boolean Logic
Mathematical Inversion as Form-Finding Strategy: John Pickering
A Combined Approach to Virtual Presence
Fabrication Strategies: Advantages and Constraints
Fabrication Strategy 1: Unrolling Surfaces to Small Panels Using Dual Graphs (186 Panels)
Fabrication Strategy 2: Unrolling Surfaces into Long Panels Defined by Geodesic Lines (60 Panels)
Historical Traces of Gaudí’s Method to French Baroque Construction
Conclusions
References
Chapter 10: An Introduction to Solid Tessellations with Students of Architecture
Introduction
Polyhedra and Solid Tessellations
The Assignment
Phase 1: Modelling the Tessellation
Phase 2: Incorporating the Polyhedral Composition within the garden’s Context
Phase 3: Definition of the Structure’s Materiality
Phase 4: Presentation of the Project
A Selection of the Projects Developed by the Students
Project a: Stopping Point
Project B: Through the Gradient
Project C: (In)Tangible
Conclusions
References