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Klein bottle

In mathematics, the Klein bottle (/ˈklaɪn/) is an example of a surface with no distinct inside or outside. In other words, it is a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. More formally, it is an example of a non-orientable surface, a two-dimensional manifold on…

Properties, Construction & Generalizations

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Construction

Properties

Dissection

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Klein bottle

Nodes59
Edges58
Triples62
Avg. degree1.97
Density0.033898
Components1

How this topic connects Entity context

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Klein bottle

Top relations

related to Properties · 11
Klein bottle → Continuing, Euclidean, It, Klein, Like, Möbius, R3, R4, R5, Unlike, While
related to External links · 9
Klein bottle → Bottle, Felix Klein, Free University Berlin, Imaging Maths, Klein, Leibniz University Hannover, OS, The Klein BottleThe, XScreenSaver
related to 3D pinched torus / 4D Möbius tube · 8
Klein bottle → In, It, Just, Klein, Möbius, One, The, Unfortunately
related to Simple-closed curves · 6
Klein bottle → Klein, Möbius, One, This, Up, Z2
is a · 5
Klein bottle → non-orientable version of the solid torus, plane R2.The fundamental group of the Klein bottle can be determined as the group of deck transformations of the universal cover and has the presentation, quotient space described as the square, similar construction, two-dimensional manifold which is not orientable
related to Construction · 5
Klein bottle → Klein, Note, The, This, To
related to Generalizations · 5
Klein bottle → Cartesian, In, Klein, Möbius, The
related to Dissection · 4
Klein bottle → Dissecting, Klein, Möbius, Remember
related to The figure 8 immersion · 4
Klein bottle → It, Klein, Möbius, To
related to Homotopy classes · 3
Klein bottle → Klein, Regular, The

Important terminology Word statistics

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Important terminology

klein bottle torus one möbius immersion space surface two plane strip cannot non-orientable parametrization figure three dimensions figure-8 embedded like

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Klein bottleis asimilar construction0.90text
Klein bottleis aquotient space described as the square0.90text
Klein bottleis atwo-dimensional manifold which is not orientable0.90text
Klein bottleis aplane R2.The fundamental group of the Klein bottle can be determined as the group of deck transformations of the universal cover and has the presentation0.90text
Klein bottleis anon-orientable version of the solid torus0.90text
Klein bottlerelated to 3D pinched torus / 4D Möbius tubeThe0.60section
Klein bottlerelated to 3D pinched torus / 4D Möbius tubeKlein0.60section
Klein bottlerelated to 3D pinched torus / 4D Möbius tubeIt0.60section
Klein bottlerelated to 3D pinched torus / 4D Möbius tubeUnfortunately0.60section
Klein bottlerelated to 3D pinched torus / 4D Möbius tubeIn0.60section
Klein bottlerelated to 3D pinched torus / 4D Möbius tubeOne0.60section
Klein bottlerelated to 3D pinched torus / 4D Möbius tubeMöbius0.60section

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