Iconography and iconology are fundamental domains when it comes to understanding artifacts of cultural heritage. Iconography deals with the study and interpretation of visual elements depicted in artifacts and their symbolism, while iconology delves deeper, exploring the underlying cultural and historical meanings. Despite the advances in representing cultural heritage with Linked Open Data (LOD), recent studies show persistent gaps in the representation of iconographic and iconological statements in current knowledge graphs (KGs). To address them, this paper presents IICONGRAPH, a KG that was created by refining and extending the iconographic and iconological statements of ArCo (the Italian KG of cultural heritage) and Wikidata. The development of IICONGRAPH was also driven by a series of requirements emerging from research case studies that were unattainable in the non-reengineered versions of the KGs. The evaluation results demonstrate that IICONGRAPH not only outperforms ArCo and Wikidata through domain-specific assessments from the literature but also serves as a robust platform for addressing the formulated research questions. IICONGRAPH is released and documented in accordance with the FAIR principles to guarantee the resource's reusability. The algorithms used to create it and assess the research questions have also been made available to ensure transparency and reproducibility. While future work focuses on ingesting more data into the KG, and on implementing it as a backbone of LLM-based question answering systems, the current version of IICONGRAPH still emerges as a valuable asset, contributing to the evolving landscape of cultural heritage representation within Knowledge Graphs, the Semantic Web, and beyond.