The Castle of Old One

Five-fold symmetry plays a central role in Lovecraft's "Beyond the Mountains of Madness". Because the five-fold symmetry is not so common in nature as three-, four-, and six-fold symmetry, it evokes blasphemous and unnatural images. Any textbook of crystallography states that there is no crystal with five-fold symmetry.
However, in the early 80's, it was discovered that some amorphous alloys show diffraction pattern with five-fold symmetry. This discovery gave birth to a new concept of "quasicrystal". The most famous example is the Penrose tiling: see http://www.lbl.gov/wonder/rotenberg-2.html for actual images.
I think the city of the Old Ones had been designed based on Penrose tiling. HPL states that star-shaped buildings could be seen here and there in the city. This statement completely matches the structure of Penrose tiling. Note that the aperiodic tiling problem is NP-complete, that is, to construct large cluster of tiling, exponentialy increasing amount of computation is needed. Thus the vastnes of the city of Old Ones indicates the highly developed technology.

BTW, there is a star-shaped castle called "Goryokaku" in Japan, which had been built by the resistants who opposed the Meiji-government in the late 19C. http://www.goryokaku-tower.co.jp/rekisi/kouzou.html
It is said that the resistants were followers of Old Ones, and they designed the castle after a secret knowledge from Necronomicon. Fortunately, they had been defeated before the construction of the castle was completed. Had it been completed, it would have been an impregnable stronghold beyond human understanding.