Cell aggregates and soap films

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.