The square has three identification spaces - three topological shapes that can be produced by gluing opposite sides to each other.
This triptych features all three - the Torus, the Klein Bottle and the Projective Plane - in a selection of interesting immersions into 3 dimensions.
This Klein Bottle is not the standard «swan neck» immersion - instead, this Figure 8 immersion highlights the structure of a circle bundle over the circle, an algebraic topological feature of the Klein bottle that plays a fundamental role in developing modern homotopy theory.
The steel version of this was
exhibited at the Joint Mathematics Meetings 2019.