Möbius strip, plate.
The Möbius strip is a surface with only one face and one edge. It is non-orientable, i.e. one cannot distinguish between up and down or inside and outside. The Möbius strip can be obtained by glueing the ends of a paper strip together after having rotated one end 180$^\circ$.
Topologically, the Möbius strip can be defined as a unit square where the upper and lower edge are identified via the equivalence relation $(x,0)\sim(1-x,1)$. This identification corresponds to the rotation prior to the glueing.
The Möbius strip has been first described by Johann Benedict Listing and August Ferdinand Möbius independently in the year 1858. Listing was a student of Gauß' and had been a professor for physics in Göttingen since 1839.
Showcase of this model is Case number 28
Hilbert, D.; Cohn-Vossen(1932). Anschauliche Geometrie, Springer-Verlag, Berlin, p. 269 f.. Online version