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 foam [1]. Kelvin's proposed tetrakaidecahedron actually had some slightly curved which is an improvement over the typical flat-faced polyhedron pictured above [2].
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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 foam [1]. Kelvin's proposed tetrakaidecahedron actually had some slightly curved faces which was an improvement over 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 23:04, 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].

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 foam [1]. Kelvin's proposed tetrakaidecahedron actually had some slightly curved faces which was an improvement over 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 the 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 space-filling geometry with even less surface area in a Philosophical Magazine Letters article. The Weaire-Phalen geometry was used as the structure for the Beijing Aquatic Center "the water cube." [3]

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).