page_title: Boy's surface
section_title: Model at Oberwolfach
hierarchical_section_title: Boy's surface / Model at Oberwolfach
caption_attribution_description: English: The Boy's Surface at the Mathematical Research Institute of Oberwolfach Deutsch: Die Boy-Fläche am MFO Русский: Модель погружения проективной плоскости в Обервольфахе.
context_page_description: In geometry, Boy's surface is an immersion of the real projective plane in 3-dimensional space found by Werner Boy in 1901. He discovered it on assignment from David Hilbert to prove that the projective plane could not be immersed in 3-space.
  Boy's surface is discussed in Jean-Pierre Petit's Topo the world. Boy's surface was first parametrized explicitly by Bernard Morin in 1978. Another parametrization was discovered by Rob Kusner and Robert Bryant. Boy's surface is one of the two possible immersions of the real projective plane which have only a single triple point.
  Unlike the Roman surface and the cross-cap, it has no other singularities than self-intersections.
context_section_description: The Mathematical Research Institute of Oberwolfach has a large model of a Boy's surface outside the entrance, constructed and donated by Mercedes-Benz in January 1991. This model has 3-fold rotational symmetry and minimizes the Willmore energy of the surface.  It consists of steel strips which represent the image of a polar coordinate grid under a parameterization given by Robert Bryant and Rob Kusner. The meridians (rays) become ordinary Möbius strips, i.e. twisted by 180 degrees. All but one of the strips corresponding to circles of latitude (radial circles around the origin) are untwisted, while the one corresponding to the boundary of the unit circle is a Möbius strip twisted by three times 180 degrees — as is the emblem of the institute (Mathematisches Forschungsinstitut Oberwolfach 2011).
caption: Model of a Boy's surface in Oberwolfach
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