## Form and Deformation

This project launches an investigation into three-dimensional forms. We will begin with an inquiry into regular convex polyhedra. Polyhedra is a geometric term that can be used to define any three-dimensional form made up of two any number of dimensional polygons. Regular polyhedra are a special set of polyhedra, where all faces are the same geometry with equal dimensions and all angles in the three-dimensional form are equal.

Regular convex polyhedra, frequently referenced as “Platonic” solids, are featured prominently in the philosophy of Plato, who spoke about them, rather intuitively, in association to the four classical elements (earth, wind, fire, water… plus ether). However, it was Euclid who actually provided a mathematical description of each solid and found the ratio of the diameter of the circumscribed sphere to the length of the edge and argued that there are no further convex polyhedra than those 5: tetrahedron, hexahedron (also known as the cube), octahedron, dodecahedron and icosahedron.

We are already familiar with cubes – one of the platonic solids – and we will further our understanding in the investigation of Archimedean solids.

We will engage in the construction of a three-dimensional form and then the strategic deformation of the volume. The project establishes rigor in model-making craft and develops three-dimensional orthographic drawing techniques. The drawings will precisely describe the deformation in the model. In this project, students will work back and forth between model and drawing, challenging and collapsing the relationship between the two modes of representation. The processes of folding/unfolding could be considered one example of the relationship between drawing and model under the topic of form/deformation. (Note: This project will serve as the midterm submission for the course.)

In order to better understand these forms, we will develop methods of fabrication and representation. We will develop methods of fabrication in surface-based models of polyhedra to gain a further understanding of the relationship between two-dimensional geometric patterns/configurations and three-dimensional constructions.

Download project brief for part 2-1 as .pdf file – *cuinda.com credentials required

Download slides from 2-1b – *cuinda.com credentials required

Digital submissions here – *cuinda.com credentials required