|How do they fill space?||Kelvin truncated octahedron||P42a||Weaire-Phelan structure|
Each face is shared in general by two different bubbles. If we decide to use different colours for bubbles of different type, the colour of each face will be determined by the bubbles that have that particular face in common.
Consider Kelvin's truncated octahedron. All its faces are of the same colour, which means that this bubble fills space by repeating copies of itself.
The Weaire-Phelan structure has two kinds of bubble, a dodecahedron (12 faces) and a tetrakaidecahedron (14). Since the dodecahedron is surrounded by tetrakaidecahedra only, its faces are light-yellow.
This row is reported here for reference.
Colour code [quadrilaterals-pentagons-hexagons]:
|Number of bubbles in the periodic unit||1||14||8|
|Number of different types of bubble||1||4||2|
|Average number of faces||14||96/7=13.714...||13.5|
|Space group (determined with Systre)||Im-3m (229)||C12/c1 (15)||Pm-3n (223)|
|Cost (computed with the Surface Evolver)||5.306||5.303||5.288|
|Reference||Acta Math. 11 (1887) 121-134||Phil. Mag. Lett. 89:8 (2009) 483-491||Phil. Mag. Lett. 69:2 (1994) 107-110|
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