According to string theory, spacetime as we know it isn't 4-dimensional, but 10-dimensional.  The next question is, where are the extra 6 dimensions that we don't see?  One answer is that they're 'compactified': roughly speaking, rolled up into such a small shape that they're unobservable by humans.
Calabi-Yau spaces may be that submicroscopic shape.  There are many such spaces, but being 6-dimensional, they're not easy to draw!  This model is a 3D cross-section through a likely space.  Surprisingly it's beautiful – a wildly self-intersecting ride.