other patterns

On the sides of a dodecahedron one can apply other line patterns of the 5-fold symmetry group. A possibility is to create touching 5-pointed stars.

other polyhedrons

While the possibilities of regular polyhedrons are limited one experimented with other polyhedrons, like the half regular Archimedean solids. These consist out of two or more regular polygons providing additional possibilities for domes. Twelve pentagons and twenty hexagons form a truncated icosahedron. Projecting the sides on a dome allows to combine 5-pointed and 6-pointed stars. Cutting the angles of a cube creates a truncated cube with eight octagons and eight triangles. In both solids you can see other combinations of polygons than in planar tilings. As a result dome patterns show other line patterns too.
truncated icosahedron (left) and truncated cube (right)
truncated icosahedron (left) and truncated cube (right)