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Sphere Inside Out
Looks like YouTube might actually be useful at something in the end ...

When I was young undergraduate math student I often wished that one day technology would allow me to project outside myself some kind of holographic animations of what I had in mind. A bit like creating the below video, store them and show them to students, not by spending ages playing around with computer animation softwares but just by thinking of them. Additionally, being able to do this interactively, as student are asking questions, would have been priceless for the student themselves, but also an endless source of pleasure for the teacher...

As I have a very geometrical mind, this could have been used, few years later, not only when I was tutoring in topology, but also while teaching most of algebra.