Beyond the Cube

Writing about the history of polyhedra up to the year 1900 means either lining up repetitive quotations from some 400 editions of Euclid's Elements or — which the author prefers — making a voyage of exploration through historic objects and images of polyhedral shapes and considering the specialists involved. Indeed, the very materialization of polyhedral form as a two-dimensional image or a three-dimensional object turns out to be one of the keys to the significance of polyhedra in history.

Core structure

• Natural Crystals
• The Earliest Polyhedral Objects
• The Ancient Greeks on Polygons
• The Ancient Greeks on Polyhedra
• Ancient Polyhedral Models
• Medieval Approach

Main ideas

• The history of mathematics did not start with Pythagoras, who built upon the theoretical and practical knowledge of geometry that the Egyptians had developed.
• After natural crystals, the next step is the man-made polyhedral object.
• In a hypothetical chronology, the ancient science of polygons and polyhedra began only after craftsmen had made simple polyhedral objects like the early cuboctahedra.
• The Greeks began to theorize about the relationship between polygons and polyhedra, and in this way entered into a hermetic realm of knowledge.

Why it matters

The materialization of polyhedral form — as image or object — is one of the keys to the significance of polyhedra in history, providing the deep geometric lineage behind Fuller's own work in synergetic geometry.

Sources

• beyond_the_cube/index.md — book project directory (repo-local source tree)
• beyond_the_cube/ — source project root