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
Einstein solid Walther Nernst learned of Einstein's 1906 paper on specific heat, he was so excited that he traveled all the way from Berlin to Zürich to meet with him. The heat capacity of an object at constant volume "V" is defined through the internal energy "U" as formula_3, the temperature of the system, can be found from the entropy To find the entropy consider a solid made of formula_5 atoms, each of which has 3 degrees of freedom. So there are formula_6 quantum harmonic oscillators (hereafter SHOs for "Simple Harmonic Oscillators"). Possible energies of an SHO are given by or, in