Then I set the students a project to create a design for either the floor of nave or sanctuary in a simple basilica style church... The results are very impressive. After one semester they are producing church floor designs that would grace any church in the country and which are more involved than most churches built in the last hundred years at least.
Here is an example of this kind of floor tiling, showing quincunxes, found at the Cathedral Basilica of Saint Louis.
The principles needed to create attractive geometric patterns are simple to learn and are ancient. Some of these rules can be found here, and the principles of Boethian proportion are also important. Some rules are indeed social convention, and an artist making art for a Catholic church ought to follow the Church's conventions. But other rules are akin to laws of nature: color is rather subjective yet still follows laws, while geometry has a truth that transcends nature and so cannot be violated.
Simple geometric construction techniques are essential for creating interesting and visually harmonic patterns. But these techniques are not necessarily apparent on visual inspection of a finished work.