Only four basic rules apply for creating concept image designs of the exterior of the USS Enterprise. The ship design requires (1) a saucer-shaped main hull with a diameter of about 20 times the thickness, (2) three long cylindrical-like sections arranged in a triangle with the larger of these three on the bottom, (3) the upper two cylindrical-like sections are connected to the main cylindrical-like section with one connecting bar each, and (4) the saucer-shaped main hull and main cylindrical-like section are connected with one connecting bar.
There have been many versions of the USS Enterprise in the Star Trek science fiction. And many individuals not associated with the production of Star Trek have dreamed up their own versions of the Enterprise. The esthetics that can be employed in the design of the USS Enterprise are limitless. Shown below are some variants of the external ship design as conceived by artists. Just keep scrolling! (Links to sites for image credits are listed at the end of this page as best I could find them.)
Rolfy the science dog (… he wonders, “Can we stop yet?”)
Links to image credits above: