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We study embedding of closed totally geodesic hyperbolic 2-orbifolds in theBianchi orbifolds $\mathbb{H}^3/PSL(2,\mathcal{O}_d)$. Our main result showsthat there is a constant $c$ such that for $d$ large enough there are at least$cd$ closed embedded totally geodesic hyperbolic 2-orbifolds. Moreover weprovide a list which conjecturally consists of those $d$ for which$\mathbb{H}^3/PSL(2,\mathcal{O}_d)$ does not contain a closed embedded totallygeodesic hyperbolic 2-orbifold.

Embedding closed totally geodesic surfaces in Bianchi orbifolds