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Schwarz's Polyhedron

SchwarzsPolyhedron

A polyhedron constructed by ruling 2n equally spaced vertical lines along the surface of a cylinder together with 2n^3 circles around the cylinder at equally spaced heights. Amazingly, joining neighboring points in triangles and letting n->infty gives a surface whose total surface area approaches, not that of the cylinder, but infinity.

See also

Cylinder

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References

Ogilvy, C. S. Tomorrow's Math: Unsolved Problems for the Amateur, 2nd ed. New York: Oxford University Press, 1972.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 224-225, 1991.

Referenced on Wolfram|Alpha

Schwarz's Polyhedron

Cite this as:

Weisstein, Eric W. "Schwarz's Polyhedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SchwarzsPolyhedron.html

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