There is a critical need for novel and made-to-order materials capable to address current and upcoming ecological, energetic, and economical global challenges pertaining to gas storage and separation and also catalysis, sensing, pollutant remediation, and more. For those purposes, materials with novel topologies must be assessed but first imagined and assembled. In this work, we propose 13 promising topologies, unveiled thanks to a rational but yet very simple method, relying on the systematic face decoration of edge nets. Nine of these topologies are disclosed for the first time, and many more can be obtained using the same methodology. We demonstrate their relevance to reticular chemistry by proposing hypothetical structures matching some of the promising topologies, all comprising readily accessible and known building blocks.