In the land of the Polytopes – Boole, Coxeter, Escher, Go….

Jenn – Fritz Obermeyer

Fritz Obermeyer’s Jenn is a nicely crafted java application that allows a playful examination of structures in non-Euclidian space, more specifically Coxeter polytopes in stereographic projection. These complex geometric structures are the 4-dimensional Sisters to the polyhedra and have, what seems like, recursive interiors and packing formations that resemble bubbles in foam.

The applet allows you to fly through these structures and orient the camera view according to your whims; other controls include toggles for the kind of rendering display settings. Perhaps I shouldn’t report it, but there are also some nice rendering glitches on some of the selected models on certain views.

The word ‘polytope’ was introduced by Alicia Boole Stott, the daughter of logician George Boole. So the story goes, she had a remarkable understanding of 4- dimensional geometry (X,Y,X,Time) from an early age. By the age of 18 she worked out by herself the six regular polytopes and built cardboard models of their sections. Later on she would meet and work with Harold Coxeter whose algorithms were employed in Jenn.

You might experience a feeling of non-Euclidean déjà vous while roaming around Jenns polytope space, the experience of space is a lot like being in one of Escher’s drawings. And neatly enough, ‘Coxeter met M. C. Escher in 1954 at a mathematics conference in Amsterdam. Escher had heard about Coxeter’s work on shapes in
Multidimensional space and sought him out. After the conference, Coxeter sent Escher a copy of his paper ‘Crystal Symmetry and Its Generalizations’ which was illustrated with complex geometric figures, including a circle containing a pattern of objects that grew smaller and smaller as they neared the edge.’

Inspired, Escher used this figure as a source for his series of ‘Circle Limit’ etchings. Coxeter and Escher remained friends until the artist’s death in 1972. It also worth noting that Coxeter was in good contact with another Dataisnature fave, Bucky Fuller, Fuller dedicated his book, Synergetics to geometrician.

After you’ve finished with Jenn, why not try your skill at Jenngo, a version of every combinatorialist’s favorite board game, Go, where the board is embedded in projective 3d-space! (download it on the same page). Afterwoods, treat yourself to a collection of Psycholudological snacks at Socialfiction, specifically those posts marked with the tag ‘Go’ and find out what its ALL about.

Connecting onward flights:
Exotic Geometries: Paper Tessellations and Spidrons.
Spacelike tessellations of tetrahedrons
Exotic mathematical surfaces.