Platonic solid the inradius "r". That is, The following table lists the various radii of the Platonic solids together with their surface area and volume. The overall size is fixed by taking the edge length, "a", to be equal to 2. The constants "φ" and "ξ" in the above are given by Among the Platonic solids, either the dodecahedron or the icosahedron may be seen as the best approximation to the sphere. The icosahedron has the largest number of faces and the largest dihedral angle, it hugs its inscribed sphere the most tightly, and its surface area to volume ratio is closest
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