Final answer:
The question seems to mix the concept of Augustine's Rule with physical structures. The Rule of Saint Augustine outlines principles of monastic life, and its enduring 'structures' are its impact on religious orders and theological thought.
Step-by-step explanation:
The question seems to refer to the Rule of Saint Augustine, a set of precepts for religious life often attributed to Augustine of Hippo. However, the question may include some confusion as it refers to "permanent structures", which could suggest a misinterpretation since the Rule itself is a document, not a physical structure.
To address the possible confusion, it's helpful to know that Augustine made significant contributions to the Christian church, some of which included the construction of physical structures, as well as establishing theological and ecclesiastical frameworks. Nonetheless, if we strictly discuss the Rule of St. Augustine, its central tenets are communal life, shared property, prayer, and work which have been foundational to various religious communities.
One could interpret "permanent structures" metaphorically as the lasting impact of the Rule on monastic communities. Moreover, Augustine's work, such as The City of God, has been an enduring 'structure' in Christian thought. Lastly, physical structures like the Basilica of St. Denis were influenced by theological ideas from church figures, including Augustine's teachings, reflecting how the ecclesiastical influenced the architectural.