The klein bottle is a surface with only one side. It's just about to enclose a space like a regular bottle, then it curves back with a twist so the inner side of the surface merges with the outer, and suddenly it doesn't enclose any volume at all.
This steel/bronze model by Bathsheba Grossman looks beautiful, is durable, washable, and sized to fit your hand, and yes, it actually opens bottles!
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Mathematics illuminates the patterns that abound in our world. The National Museum of Mathematics strives to enhance public understanding and perception of mathematics. Its dynamic exhibits and programs will stimulate inquiry, spark curiosity, and reveal the wonders of mathematics.