A Klein bottle is a 2-dimensional manifold.  It can&#x27;t be embedded in R3, but it can be embedded in R4.  This is not what people normally mean by &quot;4d&quot;, though.  It is like a Moebius strip in that they are both 2-dimensional non-orientable manifolds, though of course a Moebius strip can be embedded in R3.  The Moebius strip has a boundary, which sometimes excludes it from a strict definition of &quot;manifold&quot;.