Star dome slices

Last night I passed some time thinking and sketching out some drawings on how to divide a stardome in regular slices. This is my quick late-night sketch, but today together with my son we've done some handmade paper models as a little homeschooling practice and as a reference for further practical considerations.

As we were building the slices I notices some interesting patterns that could come out handy in various other applications: check out the following "square" pattern, made out of 2 pentagons, 2 hexagons and 6 triangles, symmetrically placed along the diagonals.

So, following my sketches we have created 4 different sections built along the main arches. They are all multiples of 36 (1/10 of a round angle) so they are also entire divisions of a dome:
36º  yellow  , 72º  red  , 108º  blue  , 144º  orange ,

 1/5 dome,   2/5 dome,  3/5 dome,     4/5 dome.

There are two complementary pairs, forming together 180º (a whole stardome):72º + 108º = 36º + 144º = 180º but you can make a full star-ball if you prop them up, all together like this.

                             144º + 36º                                                              72º + 108º 

Each pattern has some interesting symmetry along the central axis.
They're all very inspiring. Check them out.

144º

36º

108º

72º