Möbius strip (Rob Beckett)
My favourite ‘shape’ is the one sided non-orientable surface called the Möbius strip. This can be created by simply twisting a long strip of paper and gluing the ends together. One of the explanations most regularly associated with the Möbius strip is that of MC Escher, who described an ant crawling along its surface. The ant would be able to do this and return to his starting point having not even crossed an edge (or maybe it keeps crawling on indefinitely hoping to find the end!).
In the Numberphile video Möbius bridges and buildings Carlo H Séquin (UC Berkeley) considers using the idea of a Möbius strip to create aesthetic bridges and buildings.