TITLE: What are those 'others' in 'the classification table of algebraic three-folds'
QUESTION [5 upvotes]: In the Wikipedia page for 'Kodaira dimension', there is 'the classification table of algebraic three-folds' in the section 'Any dimension'.
What are those 'others'  in the very bottom of this table?
Are there some classifications for these 'others'?
Are there any examples of  these  'others' that are not rational or birational to Fano threefolds?

REPLY [4 votes]: Here is a different example. Let $S$ be an Enriques surface. Then $X = S \times \mathbb{CP}^1$ is uniruled, hence has Kodaira dimension $-\infty$. But $b_{1}(X) = 0$, hence the irregularity satisfies $q(X) = h^{0,1}(X)=0$.  Then we can can conclude that $X$ is not rational or birational to any Fano since for example $\pi_{1}(X) = \mathbb{Z}_{2}$.