# gregory mcshane

Professor of Mathematics
Institut Fourier
Grenoble, France

I am a professor at the Institute Fourier in Grenoble, France. My research interests are in low dimensional topology, dynamics but I spend a lot of time thinking about mathematical art and visualization.

Though I have been interested in visualization since 1990, when I visited the Geometry Center in Minneapolis, I only started working in 3D around 2000. Most of my 3D work is concerned with seeing features of dynamical systems - limit sets, geodesics, circle packings, etc. - and I use free software Blender and Inkscape to do this.

In 2014 I began working with wood and paper using laser cutters to craft decorative pieces - platonic solids and tessallations.

Twisting dodecahedron
12 x 12 x 12 cm
Laser cut medium density fibre board (MDF)
2015

The dodecahedron is one of the five platonic solids - it has 12 identical faces. This piece is part of a series of works representing the dodecahedron and the icosahedron in wood. The sculpture consists of 12 identical parts cut from a sheet of 3mm thick MDF. The parts are joined together along their edges just like the pieces of a jigsaw puzzle. The wood is cut to give it a degree of flexibility so that these joints can be made in 3-dimensional space and not in the plane as with a normal jigsaw puzzle.

This work is inspired by the products of the Swiss company Dutka.

Snowflake dodecahedron.
12 x 12 x 12 cm
MDF
2016

This piece is part of a series of works representing the dodecahedron and the icosahedron in wood. The sculpture consists of 12 identical parts cut from a sheet of 3mm thick MDF. The parts are joined together along their edges just like the pieces of a jigsaw puzzle. The wood is cut to give it a degree of flexibility so that these joints can be made in 3-dimensional space and not in the plane as with a normal jigsaw puzzle. In addition, we have added a 'snowflake' decoration on each face.

Heisenberg group fly through.
WebGL
2016

This is a WebGL incarnation of the static visualization of the geometry of the Heisenberg group in my other submission. After a minimal amount of tweaking the 3D model is exported using the bend4web plugin which allows one to create and display interactive 3D computer graphics in web browsers. As opposed to the static model one can rotate, zoom and even 'fly-through' the resulting model.