Given a tile $T$ in a tiling $T$, the $0$-corona of $T$ is just $C0(T)={T}$. The $n$-corona of $T (n>0)$ is $C_n(T)=\{ S \in T | S \textrm{ has nonemtpy intersection with some tile in } C_{n-1}(T) \}$. Coronae can also be defined by starting with other objects in a tiling, like coronae of clusters, edges, vertices…. rather than tiles. The $1$-corona of a vertex is also called vertex star.
Sometimes the definition of a corona reads ‘$S$ shares a full edge (face, facet) with some tile…’ instead of ‘$S$ has nonempty intersection with some tile…‘.