2-Manifold Sculptures

Carlo H. Séquin
Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (2015)
Pages 17–26

Abstract

Many abstract geometrical sculptures have the shape of a (thickened) 2D surface embedded in 3D space. A fundamental theorem about such surfaces states that their topology is captured with just three parameters: orientability, genus, and number of borders. When trying to apply this classification to interesting sculptures of famous artists depicted on the Web, a first non-trivial task is to establish an unambiguous 3D model based on which the three topological parameters can be determined. This paper describes some successful, practical approaches and gives the results for sculptures by M. Bill, C. Perry, E. Hild, and others. It also discusses the surprising topological equivalences that arise from such an analysis.

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