Non-Orientable Genus-k Surface
Non-Orientable Genus-k Surface is a topological surface, given by a parametrisation, immersed.
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aperiodic closed closed-nonorientable def-parametric immersed implemented non-orientable topological tradition-classical
Properties
- Family
- topological
- Given by
- a parametrisation
- Curvature
- no condition imposed
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Orientable
- no
- Fidelity
- exact
Definition
No chart is stored: built by mesh surgery -- cut k disks from a sphere and weld each boundary circle to itself antipodally; exact topologically, but there is no formula to store. The shipped implementation is authoritative; an unverified transcription would silently define a different surface.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- The classification theorem of closed surfaces; W. von Dyck, 'Beitrage zur Analysis situs', Math. Ann. 32 (1888) for N_3.