Schwarz lanterns

A Schwarz "polyhedron" is a polyhedral surface built on a regular cylindrical grid made of 2n lines and 2n³ circles; it is a way to approach the lateral surface of a cylinder with an assemblage of isosceles triangles.
When n tends towards infinity, the area of this folded surface tends towards infinity and not to the cylinder's lateral surface area.

On this animation only part of the polyhedral surface is represented; less circles allows a better view of the assemblage of the triangles.

reference: The Penguin Dictionary of Curious and Interesting Geometry by David Wells (Penguin, London - 1991)  pages 224-225

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updated 12-11-2003