This is the second in my series on presenting four-dimensional objects as art. The amazing Klein bottle is an object in which the INSIDE IS THE OUTSIDE. Therefore, in our three dimensional Euclidean space, it is a bottle that can hold no liquid. In four-dimensional space, however, it can. This structure has fascinated me since my university days (way back when the earth was still cooling). The Klein bottle was first described in 1882 by the German mathematician Felix Klein. The Klein bottle can be constructed by joining the edges of two Möbius strips together, as described in the following anonymous limerick: A mathematician named Klein Thought the Möbius band was divine. Said he: "If you glue The edges of two, You'll get a weird bottle like mine." In the three dimensional space we inhabit, the Klein bottle can only be constructed in a mathematical sense, and that construction is the rendering you see here. It cannot be physically constructed because this cannot be done without allowing the surface to intersect itself. Like the Möbius strip, the Klein bottle is a two-dimensional differentiable manifold, which is not orientable. Unlike the Möbius strip, the Klein bottle is a closed manifold, meaning it is a compact manifold without boundary. While the Möbius strip can be embedded in three-dimensional Euclidean space, the Klein bottle cannot. It can be embedded in four-dimensional space, however, as depicted here. It is for this reason that this rendering is an optical illusion. It can also be constructed by folding a Möbius strip in half lengthwise and attaching the edge to itself. Six colors suffice to color any map on the surface of a Klein bottle; this is the only exception to the Heawood conjecture, a generalization of the four-color theorem, which would require seven. To illustrate this amazing fact, exactly six colors are used in this rendering, and notice that the same color is never next to itself.