3 papers
math.MG2026
An immersed flat polyhedral Klein bottle
Stepan Paul
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…
math.GT2025
A piecewise-linear isometrically immersed flat Klein bottle in Euclidean 3-space
Stepan Paul
We present numerical polyhedron data for the image of a piecewise-linear map from a zero-curvature Klein bottle into Euclidean 3-space such that every point in the domain has a nei…
math.HO2021
The Flat Klein Bottle Rendered in Curved-Crease Origami
Stepan Paul
We introduce a simple and concrete way of visualizing in three dimensions a "flat" Klein bottle -- one whose local intrinsic geometry is the same as that of a flat plane -- which p…