We consider unions of interior disjoint discs in the plane such that the graph whose vertices are disc centers and edges connect centers of mutually tangent discs is triangulated, called compact packings. There is only one compact packing by discs all of the same size, called the hexagonal compact packing. It has been proven that there are exactly $9$ values of $r$ which allow a compact packing with discs of radius $1$ and $r$. It has also been proven that at most $11462$ pairs $(r,s)$ allow a compact packing with discs of radius $1$, $r$ and $s$. This paper shows that there are exactly $164$ such pairs $(r,s)$. 查看全文>>