Using a reverse-engineering method, we construct a meta-generalized gradient approximation (meta-GGA) angle-averaged exchange-correlation (XC) hole model which has a general applicability. It satisfies known exact hole constraints and can exactly recover the exchange-correlation energy density of any reasonable meta-GGA exchange-correlation energy functional satisfying a minimal set of exact properties. The hole model is applied to several nonempirical meta-GGA functionals: the Tao-Perdew-Staroverov-Scuseria (TPSS), the revised TPSS (revTPSS), and the recently Balanced LOCalization (BLOC) meta-GGA [LA Constantin, E. Fabiano, and F. Della Sala, J. Chem. Theory Comput. 9, 2256 (2013)]. The empirical M06-L meta-GGA functional is also considered. Real-space analyses of atoms and ions as well as wave-vector analyses of jellium surface energies show that the meta-GGA hole models, in …