6 dimensional Klein Bottle

cults3d

It is a reinterpretation of a classic model, a Klein bottle. It is a model of topological interest, it is formed by joining the two sides of a plane, inverting the edges, in the form of a moebius strip and joining the other two remaining sides. Physically it is impossible to realize without self-intersecting the resulting surface. The 3d design is also contradictory if we orient it to the manufacture by rapid prototyping because it needs a clear definition of what is empty and what is full. The rotation of the surface along its development prevents a univocal orientation of the normals that form the planes of the triangulated model. The simplest solution to allow the fabrication is to add another three dimensions to the model on its surface, so that the model is populated with small universes in the form of toroids, this allows to define a thickness from the connections of the toroids generating an understandable geometry for the machine. Each toroid is deformed by the surface tension it suffers with respect to its neighbouring toroids. The toroids are primo-sibling figures of the klein bottle in which we would only join the sides of the plane two by two in the logical way, without commuting the edges. This design is pure poetry.