Tetrakaidecahedron (Kelvin Cell)
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 foam [1]. Kelvin's proposed tetrakaidecahedron actually had some slightly curved which is 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 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]
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).
