Tetrakaidecahedron (Kelvin Cell)

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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].

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. Kelvin's proposed tetrakaidecahedron actually had some slightly curved faces in contrast to the typical flat-faced polyhedron pictured above [1].

Click here for other 14-sided poyhedra.

Click here to print a template to make your own tetrakaidecahedron!


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]


[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).