# Robert Webb

Computer graphics programmer
No affiliation
Melbourne, Australia

I remember being introduced to polyhedra in primary school. What was my fascination with them? Something about beauty arising from geometric order? I made more advanced models in secondary school, then left it behind for a long time. Years later I wrote a program to generate uniform polyhedra, then to create their stellations, then to generate and print nets for their construction, and Great Stella was born. Finally I could start making models again! Now I have two display cases overflowing with them and have refined my craft dramatically since those early days. Later I released Stella4D, revealing mind-bending 3D glimpses into the 4D world. Now anyone can explore this realm and print parts required to cut, fold and glue their own models.

Entwined
24 x 28 x 27 cm
Paper
2013

The 120-Cell is a regular 4D polytope with 120 regular dodecahedra as its sides. This model represents 21 of those cells, projected from 4D into 3D using a perspective projection. The dodecahedral cells are distorted by the projection, just like sides of a cube drawn in 2D. The model shows two rings of 10 dodecahedra (one green, one blue), showing how these rings entwine without touching. The final cell (in red) serves to hold the two rings in place and to act as a base. A stack of 10 dodecahedra could never bend into a ring in 3D, but in 4D it can, just as a stack of 4 squares can't form a ring in 2D, but can in 3D. However rings of faces of a 3D convex polyhedron could never interlock as rings of cells can in 4D!

Game of Thorns
26 x 26 x 30 cm
Metallic paper
2013

Is it a medieval weapon? An alien artefact? No, just a glimpse of a 4D regular polytope passing through our 3D world. This is a 3D cross-section of the great icosahedral 120-cell, a.k.a."gofix", having 120 great icosahedra as its sides. As such, each facial plane of the model also represents a 2D cross-section of the great icosahedron. The model consists of 13 small stellated dodecahedra. A regular one at the centre, representing the first vertex sliced as the sectioning hyperplane is pushed into the polytope, and 12 distorted ones, representing the next 12 victims, distorted because the hyperplane cuts these vertices at an angle. The metallic paper and sharp angles help to make this an imposing model indeed. Behold and expand your mind!