Anschauliche Geometrie  A tribute
to Hilbert, CohnVossen, 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 nonextendably collapsible 3ball.
Section: Polytopal Complexes
We obtain a geometric realization of a minimal 8vertex triangulation of the dunce hat in Euclidean 3space.
We show there is a simplicial 3ball with 8 vertices that is collapsible, but also collapses onto the dunce hat, which is not collapsible.

 

Model 2010.11.001
Udo HertrichJeromin and Wayne Rossman
Discrete minimal catenoid in hyperbolic 3space.
Section: Surfaces
We show a discrete constant mean curvature (in fact, minimal) net of revolution in hyperbolic 3space (in its Poincare halfspace 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
3Torus RepTile.
Section: Polytopal Complexes
Smallest known reptile which is a 3torus.
This nonconvex 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.

 