Difference between revisions of "Tetrakaidecahedron (Kelvin Cell)"
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[[Image:Tetrakaidecahedron.png|300px|center|thumb|From Wikimedia Commons.]] | [[Image:Tetrakaidecahedron.png|300px|center|thumb|From Wikimedia Commons.]] | ||
| − | In 1887, Lord Kelvin proposed that the tetrakaidecahedron was the best shape for packing equal-sized objects together to fill space with minimal surface area. Kelvin thought about this problem in the context of the bubbles which make up a foam [1]. Kelvin's proposed tetrakaidecahedron actually had some slightly curved faces which | + | In 1887, Lord Kelvin proposed that the tetrakaidecahedron was the best shape for packing equal-sized objects together to fill space with minimal surface area. Kelvin thought about this problem in the context of the bubbles which make up a foam [1]. Kelvin's proposed tetrakaidecahedron actually had some slightly curved faces which improved upon the typical flat-faced polyhedron pictured above [2]. |
[http://mathworld.wolfram.com/Tetradecahedron.html Click here for other 14-sided poyhedra.] | [http://mathworld.wolfram.com/Tetradecahedron.html Click here for other 14-sided poyhedra.] | ||
Revision as of 23:20, 30 November 2009
Definition
The tetrakaidecahedron (shown below) is a polyhedron studied in conjunction with foams and minimal surface area, space-filling shapes. The tetrakaidecahedron has 14 faces (6 quadrilateral and 8 hexagonal) and 24 vertices [1].
In 1887, Lord Kelvin proposed that the tetrakaidecahedron was the best shape for packing equal-sized objects together to fill space with minimal surface area. Kelvin thought about this problem in the context of the bubbles which make up a foam [1]. Kelvin's proposed tetrakaidecahedron actually had some slightly curved faces which improved upon the typical flat-faced polyhedron pictured above [2].
Click here for other 14-sided poyhedra.
Click here to print a template to make your own tetrakaidecahedron!
Applications
Scientists still use packed tetrakaidecahedrons as a model for regular, monodisperse foam. For example, Koehler, Hilgenfeldt, and Stone use the tetrakaidecahedron in their paper Liquid Flow through Aqueous Foams: The Node-Dominated Foam Drainage Equation.
The tetrakaidecahedron remained the best contender for a minimal surface-area, space filling shape from 1887 until 1994. In 1994, Weaire and Phalen presented a counter-example of a space-filling geometry with even less surface area in a Philosophical Magazine Letters article [2]. The Weaire-Phalen geometry was used as the structure for the Beijing National Aquatics Center, "the water cube" [3].
Whether or not anyone has discovered the space-filling shape with the absolute minimum surface area is still an open problem [2]!
References
[1] Weaire, Denis. "Kelvin and Ireland: Kelvin's Ideal Foam Structure," Journal of Physics: Conference Series 158 (2009).
[2] Weisstein, Eric. "Kelvin's Conjecture." From MathWorld--A Wolfram Web Resource.
[3] Rogers, Peter. "Welcome to the WaterCube, the Experiment that Thinks it's a Swiming Pool," The Guardian (5 May 2004).
