State-of-the-art theoretical studies anticipate a 2D Dirac system in the "heavy'' analogues of graphene, free-standing buckled honeycomb-like Xenes (X = Si, Ge, Sn, Pb, etc.). Herewith we regard a 2D sheet, which structurally and electronically resembles Xenes, in a 3D periodic, rhombohedral structure of layered AXTe (A = Ga, In; X = Ge, Sn) bulk materials. This structural family is predicted to host a 3D strong topological insulator with Z(2) = 1;(111) as a result of functionalization of the Xene derivative by covalent interactions. The parent structure GaGeTe is a long-known bulk semiconductor; the "heavy'', isostructural analogues InSnTe and GaSnTe are predicted to be dynamically stable. Spin-orbit interaction in InSnTe opens a small topological band gap with inverted gap edges that are mainly composed of the In-5s and Te-5p states. Our simulations classify GaSnTe as a semimetal with topological properties, whereas the verdict for GaGeTe is not conclusive and urges further experimental verification. The AXTe family structures can be regarded as stacks of 2D layered cut-outs from a zincblende-type lattice and are composed of elements that are broadly used in modern semiconductor devices; hence they represent an accessible, attractive alternative for applications in spintronics. The layered nature of AXTe should facilitate the exfoliation of their hextuple layers and manufacture of heterostructures.