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
BET theory physical adsorption of gas molecules. The total surface area formula_19 and the specific surface area formula_20 are given by where formula_5 is in units of volume which are also the units of the monolayer volume of the adsorbate gas, formula_24 is Avogadro's number, formula_25 the adsorption cross section of the adsorbing species, formula_26 the molar volume of the adsorbate gas, and formula_27 the mass of the solid sample or adsorbent. The BET theory can be derived similarly to the Langmuir theory, but by considering multilayered gas molecule adsorption, where it is not required for a layer to be completed before