Penrose Kites and Darts

Penrose Kites and Darts have additional rules which forbid them from being placed together in certain ways. For example, of the collection illustrated earlier, only the superkite, the angel and the crab are permissible:

and out of the 16 ways of putting a 72° angle round a point, it is only the decagon, the star, the priest and the folding chair which are in fact permissible: