# Michael Wettstein

The problem of finding the configuration of n points on a sphere
that maximize the minimal distance, or equivalently, finding the
location of n non-intersecting circles on a sphere with maximal
radius, is known as the Tammes problem. This problem is named after
the botanist L. Tammes who studied the distribution of pores on
pollen grains in 1930. Explicit solutions are known only for a
limited number of points. Through enumerating possible vertex
locations, Michi searched for solutions and verified them with
Laszlo Hars’ numerical results. Surprisingly, the vertices of two
platonic solids, namely the cube and dodecahedron, are not
necessarily arranged in an optimal way. The short film “Kugeln um
Kugel“ shows constructions of the optimal configurations for n = 1
to n = 20. The conversions of the cube, dodecahedron, and
cuboctahedron to the optimal configurations are visualized. The
music was developed in the project Megaboom – a remix of the track
“Allkugeltrain” by Rio.