A history of polyhedra up to 1900, told as a voyage through historic objects and images of polyhedral shapes rather than repetitive citations of Euclid. Treats the materialization of polyhedral form as a key to its significance in history.

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