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. | + | 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 | + | 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 | + | |
| + | [http://zapatopi.net/blog/?post=200407047160.make_your_own_kelvin_cells Click here to print a template to make your own tetrakaidecahedron!] | ||
== Applications == | == 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 | + | 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). | ||
| − | http://mathworld.wolfram.com/KelvinsConjecture.html | + | [2] Weisstein, Eric. [http://mathworld.wolfram.com/KelvinsConjecture.html "Kelvin's Conjecture."] From MathWorld--A Wolfram Web Resource. |
| − | http:// | + | [3] Rogers, Peter. [http://www.guardian.co.uk/science/2004/may/06/research.science1 "Welcome to the WaterCube, the Experiment that Thinks it's a Swiming Pool,"] The Guardian (5 May 2004). |
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].
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).
