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…‘.