We investigate here a new family of zeolitic Metal Organic Frameworks (MOFs) based on imidazole (im) as the ligand and epsilon-type Keggin PolyOxoMetalates (POMs) as building units. The POM used in this study is the epsilon-{PMo(12)O(40)} Keggin isomer capped by four Zn(ii) ions (noted epsilon-Zn) in tetrahedral coordination. We describe here our methods to first construct and then evaluate the stability of hypothetical 3-D POMOFs possessing a tetrahedral network, typified by dense silica polymorphs and zeotypes and referred here to as Z-POMOFs. We use the analogy between the connectivity of silicon ion in dense minerals or zeolites and the epsilon-Zn, using imidazolate ligands to mimic the role of oxygen atoms in zeolites. Handling the epsilon-Keggin and imidazole as the constitutive building-blocks, a selection of 40 polymorphs were constructed and their relative stabilities computed. Among these Z-POMOFs, the cristobalite-like and zni-structure were identified as the most stable candidates. In parallel, we have attempted to synthesize Z-POMOF structures with epsilon-Zn POMs, synthesized in situ under hydrothermal conditions, and imidazole ligands. We present our first experimental result, the extended material [NBu(4)][PMo(V)(8)Mo(VI)(4)O(37)(OH)(3)Zn(4)(im)(Him)], named epsilon(im)(2). The structure of the hybrid framework is built by the connection of dimerized epsilon-Zn POMs to imidazole ligands in two directions. The obtaining of the first POMOF based on imidazole ligand is an encouraging step towards the synthesis of a new family of POMOFs.