In principle, any curved optical surface can be built from a large number of small, flat plane mirrors that are properly angled to a common focal point. The problem is that the pointing of the individual mirrors must be accurate to a fraction of a wavelength of light, the individual mirrors must be optically flat to a fraction of a wavelength of light, and the mirrors must be small in size compared to the area covered to avoid 'edge effects'. Rather than tiling a parabolic form, it is easier to grind and polish it directly. If you are not interested in imaging, but just want to do spectroscopy and need a 'light bucket' you might be able to get away with tiling a surface like this.