  How many unit $n-$dimensional spheres can simultaneously touch or kiss a
central $n-$dimensional unit sphere? Beyond mathematics this question has
implications for fields such as cryptography and the structure of biologic and
chemical macromolecules. The kissing number is only known for dimensions 1-4, 8
and 24 (2, 6, 12, 24, 240, 19650, respectively) and only particularly obvious
for dimensions one and two. Indeed, in four dimensions it is not even known if
Platonic polytope unique to that dimension known as the 24-cell is the unique
kissing configuration. We have not been able to prove that the 24-cell is
unique, but, using a physical approach utilizing the hopf map from four to
three dimensions, we for the first time delimit the possible other
configurations which could be kissing in four dimensions.
