This book highlights the polytopic projects basic similarity despite the noticeable difference as domains of application. High-dimensional reference architectures presented here allows confronting and prevailing over the growing complexity of polytopic projects implementations.Self-evolvable complex systems require high dimensional polytopic reference architectures for concrete implementation. Polytopic projects target artificiality and engineering objectives for material, biological, cognitive, and intelligent systems. Polytopic roadmaps are proposed here as methods to synthesize the systemic thinking and capabilities to advance on the roads to higher complexity projects. The role of iterations, inclusions and of 4D-cubes for the reference architectures is emphasized.Non-Aristotelian Logic of Contradiction and the Included Middle are fundamental for control of different domains of higher complexity. Supramolecular chemistry, metal organic frameworks and reaction networks are presented in the frame of polytopic chemistry. Dynamical hierarchies and quasi-species are the considered biosystems. Developmental stages, formal concepts analysis, and neural coding are the focused cognitive systems. Modeling levels, the 4D digital twins, Hopf monoids, dual-graded graphs, and V-models are informally presented. Applications refer to high-dimensional separations, nesting, and drug delivery. Multi-scale transfer, distributors-collectors, cyclic operations, middle vessel columns, mixing, assembly, and dual designs are the illustrated engineering systems. Polytopic features of industry, economy, society, and sustainability as well as new domains of interest as arts and architecture, transdisciplinarity, complex systems and unity of sciences and engineering are presented.Excluded Middle and Included Middle General Polytopic Roadmaps have been proposed as exemplars of Polytopic Roadmaps for experts from various domains to synthesize their thinking and capabilities into new projects implementation, facing and exceeding complexity. A significant finding of this book is that self-evolvability roads observed in natural systems is based on the same directed sequence of reference architectures as the self-evolvability roads of concepts in our mind.Continuing and developing the ground-breaking field of self-evolvable systems and presenting roads to advance in ever growing complexity domains, the book will be useful to engineers, researchers, entrepreneurs, and students in different branches of production, complex systems science and engineering, ecology, and applied mathematics.

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