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A representation of a Klein bottle. Klein bottles are an example of a non-orientable surface, meaning there is no way to discern a proper "inside" and "outside". You could follow a path along the surface thatwould lead you back to the same place but upside-down. A true Klein bottle is not a hollow object but rather a solid defined by a single sweeping surface. Since that would be impossible in our 3-dimensional world, such objects are presented as thickened representations of their surfaces, similar to representing a solid cylinder as a hollow tube.
The Klein bottle is a unique and fascinating object, perfect to touch and explore, or to present as a display piece.