Is the opening of the NOVA program on PBS a Calabi-Yau space?
Yes, it's definitely a 2D projection of a 3D model of a Calabi-Yau space. See e.g. this one
as an example. It's an animated version of what was included in the Elegant Universe, the book, by Brian Greene which was this one:
Jeff Bryant did the animation but the algorithms to draw the individual frames is due to Andrew J. Hanson. The book version captures the 2D projection of the 3D slice through the quintic hypersurface in the 4-dimensional complex projective space – the arguably most popular Calabi-Yau three-fold among physicists (and probably the first one that was considered for a heterotic compactification by Strominger and others in the mid-to-late 1980s). Note that this surface has some parameters that may be changed to adjust the shape – we say it has a whole moduli space of shapes.
Various other morally similar pictures are meant to be Calabi-Yau surfaces, too, e.g. this one:
Even if some of them were different surfaces, they look like "the same kind of a surface" to an untrained eye – and many trained eyes, too.