Platonic solid to that of a sphere of the same size (i.e. either the same surface area or the same volume.) The dodecahedron, on the other hand, has the smallest angular defect, the largest vertex solid angle, and it fills out its circumscribed sphere the most. Every polyhedron has a dual (or "polar") polyhedron with faces and vertices interchanged. The dual of every Platonic solid is another Platonic solid, so that we can arrange the five solids into dual pairs. If a polyhedron has Schläfli symbol {"p", "q"}, then its dual has the symbol {"q", "p"}. Indeed, every combinatorial property of one
Capillary surface and that the most stable configuration can become metastable through mechanical jarring without too much difficulty. On the other hand, a metastable surface can sometimes spontaneously achieve lower energy without any input (seemingly at least) given enough time. Boundary conditions for stress balance describe the capillary surface at the contact line: the line where a solid meets the capillary interface; also, volume constraints can serve as boundary conditions (a suspended drop, for example, has no contact line but clearly must admit a unique solution). For static surfaces, the most common contact line boundary condition is the implementation of the contact