Outline
DOI: 10.1515/advgeom-2026-0017 ISSN: 1615-7168
An immersed flat polyhedral Klein bottle
Stepan PaulAbstract
We present a polyhedral surface in Euclidean 3-space with the topology of a Klein bottle such that every vertex has zero angle defect and the star of every vertex is embedded. From the perspective of metric geometry, the polyhedron can be viewed as the image of a piecewise smooth isometric immersion of a flat Klein bottle. It is apparently the first explicit such example.
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