klein dogs

The idea of owning a pet in a busy city can be daunting, but the image of a pet itself can bring comfort. I wanted to explore how far this could be taken, and decided on distilling it down to a single surface.

The Klein dog takes the one-sided 3D shape of a Klein bottle and morphs it into something that resembles our best friends. These morphologies, only possible in 4D space, can be modelled and manufactured with some difficulty. The final models were printed and finished by hand.

A Klein bottle is a closed surface with no inside and no outside: a flat two-dimensional sheet that folds back through itself until both sides turn out to be one.^[1] It only truly exists in four dimensions. Modelled in three, the surface has no choice but to pass through itself, leaving a small blip where the neck crosses the body; in 4D that intersection simply is not there, the neck arriving without ever touching the surface.^[2] Each dog wears its blip in plain sight.