Wild Translation Surfaces Project

This project aims to create an evolutive encyclopedia of concrete translation surfaces. It can be just a place to inventory existing surfaces (from the litterature or the folklore). It can also become a place of creation, a place where people collaborate to find new exotic translation surfaces.

Feel free to add new pages or modify existing pages. You can add new surfaces, ask for surfaces satisfying certain property, find new properties to an existing surface, simply add a comment, a new proof, a picture... Whatever you want!

Some translation surfaces

• Squared Snake Surface
• Two Directions Surface
• Regular Decagon
• Extraordinary Origami Curve
• Billiard With Wall
• Obtuse Veech Triangle
• Double Covered Regular Octagon
• L Shaped Surfaces
• Arnoux Yoccoz Surface
• Thurston Surface

Some properties

• No Geodesic From A Singularity To Itself
• No One Cylinder Decomposition
• Finite Blocking Property
• Simple Jinvariant Property
• Torus Branched Covering
• Complete Periodicity
• Lattice Property
• Bouillabaisse Surfaces