Synergetics is a scientific philosophy and book by Buckminster Fuller which ties together threads from the comprehensive breadth of his thinking throughout the 20th century growth of the modern age.
Geometry plays a central role because of its foundational nature in experientiality, on which science is based.
Synergetic geometry ties together myriad geometrical insights from throughout the history of the subject, but is nonstandard in that it relies on a purely experiential foundation, using nature as a guide. Natural structures are experientially dominated by angular relationships other than 90 degrees (although perpendicularity is obviously present and conceptually useful in many ways as well).
More important than the foundational geometry, however, is the emphasis in synergetic philosophy of comprehensivity in the engineering of solutions to real-world problems.
The book _Synergetics_ is a geometric demonstration of potentials in myriads of directions, many of which are speculative and potentially dubious, and many more of which reveal the implications inherent in many common and historical insights about the world.
The book is a masterpiece of idiolectic thinking out loud on paper, accomplished with the organizational assistance of Ed Applewhite.