starting from a dodecahedron
In a plane it’s not possible to realise a tiling only with regular pentagons. But in space it’s possible to create a dodecahedron with 12 regular pentagons.
On the faces of it one can create line patterns the same way as in a plane. If you project this pattern on the circumscribed sphere the result is a line pattern one can use for a domed structure. This principle was used for the north-eastern dome of the Friday Mosque in Isfahan (1088-89).
