Date started: November 2019

Leads: Sabetta Matsumoto, Pierre Arnoux, Samuel Lelièvre

Abstract

Inspired by Rich Schwartz’s lectures on translation surface and some conversations with Pierre and Samuel, I wanted to create tactile genus two translation surfaces. The first one is a rectangle suspension and the second is the double pentagon surface.

Quilted Translation Surfaces

Media

The first surface is a rectangle suspension. The pattern came from a model that Maki Furukado made for Pierre Arnaux.

This is the layout for the rectangle suspension. (Image credit: Edmund Harriss)

This is the layout for the rectangle suspension. (Image credit: Edmund Harriss)

Here is a partially completed surface. (Image credit: Edmund Harriss)

Here is a partially completed surface. (Image credit: Edmund Harriss)

This is the layout for the rectangle suspension. (Image credit: Edmund Harriss)

It is currently a punctured genus-two surface, as you can see by my hand. (Image credit: Edmund Harriss)

This is the finished object with the single "6 pi/" singularity in the center.

This is the finished object with the single "6 pi" singularity in the center.

Samuel Lelièvre requested I also make the double pentagon surface that he and Diana Davis have studied:

This is the layout for the rectangle suspension. (Image credit: Edmund Harriss)

This surface starts with two pentagons oriented like this and then parallel edges are joined together.

The double pentagon surface after the central 3 edges are joined together.

The double pentagon surface after the central 3 edges are joined together.

After the fourth edge is joined. It is still a punctured genus-one surface here.

After the fourth edge is joined. It is still a punctured genus-one surface here.

After the fifth edge is joined, the second cycle becomes apparent. The single "6 pi" singularity is in the center.

After the fifth edge is joined, the second cycle becomes apparent. The single "6 pi" singularity is in the center.