| 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]: |
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| 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.