Geometry and Topology

Minimum Energy Surfaces

Smooth Curves on Smooth Surfaces

The general topic is to make smooth curves on smooth (subdivision) surfaces. One special goal is to make a few mathematical models that demonstrate how graphs of relatively high interconnectivity can be mapped crossing-free onto surfaces of suitable genus. As one example, we will map Dyck's graph with 12 vertices and 48 edges onto a genus-3 surface.

Hi-D Regular Polytopes

Semi-Regular Polyhedra

Uniform Polyhedra

Zonohedron

Tilings R3 with Toroids

Tilings R3 with Trefoil-Knots

Topologically Important Surfaces

  1. Figure-8 Immersion of Torus
  2. Elliptical Torus of Revolution
  3. Standard Model of Klein Bottle
  4. Figure-8 Model of the Klein Bottle
  5. The Crosscap
  6. The Roman Surface
  7. Boy's Surface -- and "Boy's Planet" -- and a write-up -- and the publisher
  8. Hunt's Surface
Skeleton of a Klein Bottle
  • Benno Artmann's Topological Models

    • Page Editor: Carlo H. Séquin