H. S. M. Coxeter

British-Canadian mathematician (1907–2003), the twentieth century's foremost classical geometer, author of the standard treatise Regular Polytopes and defender of visual, model-based geometry against the abstraction of his era.

Coxeter devoted his career to polytopes, symmetry groups, and higher-dimensional figures, keeping alive a tradition of geometry grounded in visualization and physical models at a time when Bourbaki-style formalism was purging pictures from mathematics. His Regular Polytopes is the definitive account of the higher-dimensional analogues of the Platonic solids, building on the intuitive work of pioneers like Alicia Boole Stott. His life and mission are the subject of Siobhan Roberts's biography The Man Who Saved Geometry.

Role in Fuller's orbit

Coxeter is the great modern custodian of the polyhedral-and-symmetry geometry that underlies Fuller's synergetics — the tetrahedra, octahedra, icosahedra, and their symmetries. He shares Fuller's conviction that geometry should be seen and modeled, not merely symbolized, making him the mathematician's counterpart to Fuller's model-first approach.

See Also

• Regular Polytopes (Regular Polytopes) — his classic treatise
• The Man Who Saved Geometry (The Man Who Saved Geometry) — Siobhan Roberts's biography of him
• Siobhan Roberts (Siobhan Roberts) — his biographer
• Alicia Boole Stott (Alicia Boole Stott) — earlier pioneer of the polytopes whose work he built on
• Nicolas Bourbaki (Nicolas Bourbaki) — the formalist movement whose purge of visual geometry he resisted
• Keith Critchlow (Keith Critchlow) — adjacent geometer of spatial order

Sources

• Regular Polytopes (source reference) — the treatise he wrote
• The Man Who Saved Geometry (source reference) — the biography about him