Electronic Geometry Models


Electronic Geometry Models

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 2006.04.001 by Udo Hertrich-Jeromin Discrete cmc-1 surfaces of revolution in hyperbolic space.
Section: Survaces / Mean Curvature Surfaces

Two members of the 1-parameter family of discrete catenoid cousins are shown. Surfaces of constant mean curvature (cmc) are special isothermic surfaces and various features of cmc surfaces can be interpreted in terms of the transformation theory of isothermic surfaces.

Model 2005.11.001 by Udo Hertrich-Jeromin Lawson Family of a discrete Enneper surface.
Section: Survaces / Mean Curvature Surfaces

The model shows a discrete horospherical net from the 1-parameter family of a discrete Enneper net.

Model 2005.12.001 by Axel Werner Smallest non-trivial 2s2s-polytope.
Section: Discrete Mathematics / Polytopes

A polytope P is k-simplicial if all its k-faces are simplices and it is h-simple if its dual polytope PΔ is h-simplicial [2]. Therefore, a 4-dimensional polytope is 2-simplicial and 2-simple, if all 2-dimensional faces are triangles and all edges are contained in exactly 3 facets; in this case, we call it a 2s2s-polytope.

Model 2006.02.001 by Stefan Hougardy, Frank H. Lutz, and Mariano Zelke Polyhedra of Genus 3 with 10 Vertices and Minimal Coordinates.
Section: Surfaces / Polyhedral Surfaces

Coordinate-minimal geometric realizations in general position for 17 of the 20 vertex-minimal triangulations of the orientable surface of genus 3 in the 5x5x5-cube.

Model 2005.10.001 by Shoichi Fujimori and Toshihiro Shoda: Triply periodic minimal surface of genus 4 .
Section: Surfaces / Minimal Surfaces

It is known that any compact minimal surface in a flat 3-torus can be regarded as a triply-periodic minimal surface in Euclidean 3-space, and here we exhibit such a surface.

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