klein bottle in English
Gluing the top of the Möbius band to the bottom would give you a compact Klein bottle , a complicated shape that is impossible to draw properly in three dimensions.
Use "klein bottle" in a sentence
1. A closely related 'strange' geometrical object is the Klein bottle.
2. The following square is a fundamental polygon of the Klein bottle.
3. The common physical model of a Klein bottle is a similar construction.
4. The real projective plane, like the Klein bottle, cannot be embedded in three-dimensions without self-intersections.
5. BS(1, 1) is the free abelian group on two generators, and BS(1, −1) is the fundamental group of the Klein bottle.
6. On the other hand, there are surfaces, such as the Klein bottle, that cannot be embedded in three-dimensional Euclidean space without introducing singularities or self-intersections.
7. Six colors suffice to color any map on the surface of a Klein bottle; this is the only exception to the Heawood conjecture, a generalization of the four color theorem, which would require seven.