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Mathematics behind THE DOT DiadochoKinesis & Cyclic Groups from the point of view of Group Theory Operational Duties Redistribution for Minimum Number of Moving Bodies Topological Rearrangement for Maximum Degree of Engine Compactness Operational & Topological Total Optimization for Best Engine Performance Algebraic Construction of Motion Arrays of Any Ideal Operational Cycle Algebraic Construction of Tooth of Ideal Variable Transmission Ratio Gear Heuristic Search of All Structural Combinations that Satisfy Definite Specifications Algebraic Exhaustive Study of the Most Promising Structural Combinations Computing behind THE DOT Numerical Construction of Motion Arrays of Any Ideal Operational Cycle Numerical Construction of Tooth of Ideal Variable Transmission Ratio Gear Algorithmic Search of almost All (more than Three Million) Possible Structural Combinations ! Numerical Exhaustive Study (almost One Trillion Cases, in total) of the Most Promising Structural Combinations ! Forces Analysis & WireFrame Simulation of All Bodies via Doric Logic Structural & Photorealistic Simulation of Entire Engine via Pro/MECHANICA Engineering behind THE DOT Repeated Redesigning in order to be All Bodies Freely Supported at Both Ends Repeated Redesigning in order to have All Bodies Any Required Robustness Total Redesigning for achieving Required Strength of Entire Engine in Any Scale Post Redesigning in order to have All Bodies Highest Simplicity in Construction & Operation Manufacturing behind THE DOT Manufacturing of Tooth of Ideal Variable Transmission Ratio Gear via CNC Manufacturing of Tooth of Ideal Variable Transmission Ratio Gear via CAC 
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