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
Finite volume method tensor. Again we can sub-divide the spatial domain into finite volumes or cells. For a particular cell, formula_42, we take the volume integral over the total volume of the cell, formula_43, which gives, On integrating the first term to get the "volume average" and applying the "divergence theorem" to the second, this yields where formula_46 represents the total surface area of the cell and formula_47 is a unit vector normal to the surface and pointing outward. So, finally, we are able to present the general result equivalent to (8), i.e. Again, values for the edge fluxes can be reconstructed by