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Fontbonne University

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Geometry

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New Families Of Embedded Triply Periodic Minimal Surfaces Of Genus Three In Euclidean Space, Adam G. Weyhaupt Jan 2006

New Families Of Embedded Triply Periodic Minimal Surfaces Of Genus Three In Euclidean Space, Adam G. Weyhaupt

All Theses, Dissertations, and Capstone Projects

Until 1970, all known examples of embedded triply periodic minimal surfaces (ETPMS) contained either straight lines or curves of planar symmetry. In 1970, Alan Schoen discovered the gyroid, an ETPMS that contains neither straight lines nor planar symmetry curves. Meeks discovered in 1975 a 5-parameter family of genus 3 ETPMS that contained all known examples of genus 3 ETPMS except the gyroid. A second example lying outside the Meeks family was proposed by Lidin in 1990. Große-Brauckmann and Wohlgemuth showed in 1996 the existence and embeddedness of the gyroid and “Lidinoid”. In a series of investigations the scientists, Lidin, et. …