  An orbifold datum is a collection $\mathbb{A}$ of algebraic data in a modular
fusion category $\mathcal{C}$. It allows one to define a new modular fusion
category $\mathcal{C}_{\mathbb{A}}$ in a construction that is a generalisation
of taking the Drinfeld centre of a fusion category. Under certain simplifying
assumptions we characterise orbifold data $\mathbb{A}$ in terms of scalars
satisfying polynomial equations and give an explicit expression which computes
the number of isomorphism classes of simple objects in
$\mathcal{C}_{\mathbb{A}}$.
  In Ising-type modular categories we find new examples of orbifold data which
- in an appropriate sense - exhibit Fibonacci fusion rules. The corresponding
orbifold modular categories have 11 simple objects, and for a certain choice of
parameters one obtains the modular category for $sl(2)$ at level 10. This
construction inverts the extension of the latter category by the $E_6$
commutative algebra.
