Alexander’s horned sphere

Date started: September 2019
Leads: Arnaud Chéritat


How to model a smooth Alexander horned sphere (except at the tips)? At the first conference during the ICERM semester “Illustrating mathematics”, I contributed a few questions on the board on the list of “mathematical things you would like to see illustrated in geometry”. Among them I asked for the following: “make a model of Alexander’s horned sphere that is smooth (except at the tips)”. A participant approached me a few days later: it was Pr Robert Edwards from UCLA. He drew for me a sketch, of which the photo is below. In November I started to work on making a 3D mesh on this principle, which I 3D-printed with the help of Alba Malaga and Samuel Lelièvre. Greg McShane also has a design, we will try it later.


Image from Wikipedia (public domain)
Rendering with POV-Ray
Sketch by Robert Edwards
First attempt : too fragile
Second attempt: succes, with a little bit of help