|What is this page about?||Kelvin truncated octahedron||P42a||Weaire-Phelan structure|
This page displays a comparison between periodic units of models for the partitioning of three-dimensional Euclidean space into regions of equal volume with low surface area (shown as cost below).
The polygonal (face) composition of each polyhedron (solid) is given by 3 numbers [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|
Transparent, straight-edged models are also available. Using the colour code above, you can see how these units pack to fill space. For further options right-click on the image. For full screen mode, select 'New Display' then maximize the window.
Graphics by Surface Evolver and Javaview.