# 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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Archimedean Solids
Cockles
Dupin Cyclides
Elliptic Linear Congruence
Geodesics on a Cone
Helices on a Helicoid
Hyperosculating Spheres
Impossible Objects
Klein Bottle
Knots
Menger Sponge
Möbius Tetrahedra
Pascal's Pyramid
Pipe Surfaces
Planar Sections of a Torus
Platonic Solids
Prince Rupert's Cube
Schwarz Lanterns
Snails
Spherical Loxodromes
Stationary Points
Striction Curves