Difference between revisions of "Tetrakaidecahedron (Kelvin Cell)"

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== Definition ==
 
== 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]
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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].
  
 
[[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 also thought about foam in his discussion of this problem. Kelvin's proposed tetrakaidecahedron actually had curved faces in constrast with the typical flat-faced polyhedron pictured above.
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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 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.]
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== Applications ==
 
== Applications ==
  
The tetrakaidecahedron is used to model foams. Koehler, Hilgenfeldt, and Stone use the tetrakaidecahedron in their paper [[Liquid Flow through Aqueous Foams: The Node-Dominated Foam Drainage Equation]].
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Scientists still use packed tetrakaidecahedra as a model for regular, monodisperse foam. For example, Koehler, Hilgenfeldt, and Stone use tetrakaidecahedra in their paper, ''[[Liquid Flow through Aqueous Foams: The Node-Dominated Foam Drainage Equation]]''.
  
The tetrakaidecahedron filled space with the least amount of surface area from 1887 to 1994. In 1994, Weaire and Phalen presented a 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]
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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]. Architects used the Weaire-Phalen geometry in the design of the Beijing National Aquatics Center, "the water cube" [3].
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Whether or not anyone has discovered the space-filling shape with the absolute minimum surface area is still an open question [2]!
  
 
== References ==
 
== References ==

Latest revision as of 23:39, 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 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 tetrakaidecahedra as a model for regular, monodisperse foam. For example, Koehler, Hilgenfeldt, and Stone use tetrakaidecahedra 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]. Architects used the Weaire-Phalen geometry in the design of 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 question [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).