Terpenoids make up the largest class of specialized metabolites with over 180,000 reported compounds currently across all kingdoms of life. Their synthesis accentuates one of natures most choreographed enzymatic and non-reversible chemistries, leading to an extensive range of structural functionality and diversity. Current terpenoid repositories provide a seemingly endless landscape to systematically survey for information regarding structure, sourcing, and synthesis. Efforts here investigate entries for the 20-carbon diterpenoid variants and deconstruct the complex patterns into simple, categorical groups. This deconstruction approach reduces over 60,000 unique diterpenoid structures to less than 1,000 categorical structures. Furthermore, the majority of diterpene entries (over 75%) can be represented by less than 25 core skeletons. Natural diterpenoid abundance was mapped throughout the tree of life and structural diversity was correlated at an atom-and-bond resolution. Additionally, all identified core structures provide guidelines for predicting how diterpene diversity originates via the mechanisms catalyzed by diterpene synthases. Over 95% of diterpenoid structures rely on cyclization. Here a reconstructive approach is reapplied based on known biochemical rules to model the birth of compound diversity. Reconstruction enabled prediction of highly probable synthesis mechanisms for bioactive taxane-relatives, which were discovered over three decades ago. This computational synthesis validates previously identified reaction products and pathways, as well as enables predicting trajectories for synthesizing real and theoretical compounds. This deconstructive and reconstructive approach applied to the diterpene landscape provides modular, flexible, and an easy-to-use toolset for categorically simplifying otherwise complex or hidden patterns.