Solid Klein bottle

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In mathematics, a solid Klein bottle is a 3-manifold (with boundary) homeomorphic to the quotient space obtained by gluing the top of D2 x I to the bottom by a reflection, i.e. the point (x,0) is identified with (r(x), 1) where r is reflection of the disc D2 across a diameter.

Note the boundary of the solid Klein bottle is a Klein bottle.