Anschauliche Geometrie - A tribute to Hilbert, Cohn-Vossen, Klein and all other geometers.

### Electronic Geometry Models

This archive is open for any geometer to publish new geometric models, or to browse this site for material to be used in education and research. These geometry models cover a broad range of mathematical topics from geometry, topology, and to some extent from numerics.

Click "Models" to see the full list of published models. See here for details on the submission and review process.

##### Selection of recently published models

Model 2013.10.001 Bruno Benedetti and Frank H. Lutz The dunce hat in a minimal non-extendably collapsible 3-ball.
Section: Polytopal Complexes

We obtain a geometric realization of a minimal 8-vertex triangulation of the dunce hat in Euclidean 3-space. We show there is a simplicial 3-ball with 8 vertices that is collapsible, but also collapses onto the dunce hat, which is not collapsible.

Model 2010.11.001 Udo Hertrich-Jeromin and Wayne Rossman Discrete minimal catenoid in hyperbolic 3-space.
Section: Surfaces

We show a discrete constant mean curvature (in fact, minimal) net of revolution in hyperbolic 3-space (in its Poincare half-space incarnation).

Model 2010.02.002 Marina Knyazeva and Gaiane Panina Counterexample to a conjecture of Alexandrov.
Section: Surfaces

A pointed graph on the sphere which leads to a counterexample to A.D. Alexandrov's conjecture.

This graph is interesting and important not only because of its funny combinatorics, but also because it leads to a counterexample to A.D. Alexandrov's uniqueness conjecture for smooth convex surfaces.

Model 2010.02.001 Dirk Frettloeh and Iwan Suschko 3-Torus Rep-Tile.
Section: Polytopal Complexes

Smallest known rep-tile which is a 3-torus.

This non-convex polytope P is made from 12 rectangular boxes of side length 1, a, b. Two copies of P can be assembled into a rectangular box of edge length 3, 2a, 4b.