Differential Geometry and Geometric Structures
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Students' Work: Schwarz Lanterns


A Schwarz lantern is a polyhedral surface inscribed into a cylinder of revolution. It depends on two parameters: k is the number of (equal) rings; each ring is triangulated into 2n congruent isosceles triangles. As k and n both go to infinity, the triangles get smaller and smaller. But the area of the lanterns may have a limit anywhere between the area of the cylinder (e.g. when k = n) and infinity (e.g. when k = n3).
The image illustrates a cutout of the case k =30, n =4.

Created by Bernhard Skritek (2008) using POV-Ray - The Persistance of Vision Raytracer.

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