(a) Potassium reacts with C₆₀ (Fig. 4.16) to give a compound in which all the octahedral and tetrahedral holes are filled by potassium ions. Derive a stoichiometry for this compound. 

(b) The reaction of C₆₀ with excess potassium yields a material that has a body-centred arrangement of C₆₀ molecules with two potassium ions along each unit cell edge; calculate the stoichiometry of this compound.

Figure 4.16.