I'm trying to design a dome made out of pentagons but the faces won't form, please help

model2_1.skp (321.8 KB)

The edges of your polygons must lie on the same plane in order for faces to be formed. Since you aren’t getting those faces, it’s evident that the edges aren’t coplanar. You can create faces by adding edges to make triangles.

Those edges could be hidden so they don’t show but the right thing to do is create the polygons so they are planar shapes.

That looks like a regular dodecahedron cut off at the bottom.

Try my plugin Polyhedra from the Sketchucation plugin store tp draw a full dodecahedron, then cut off the bottom.

Or if you want to draw it with native tools more accurately, see a 3D Warehouse explanation. The link displays in my draft but won’t show on the forum. Here’s the diagram that explains how to do it.

It shows you how to draw one using rectangles in the Golden Ratio (approx 1.618: 1 sides - like the European and UK A series paper, of which A4 is the common size for general correspondence (approximately the same size as US Letter paper, but slightly taller and a little narrower).
Since I can’t post the link, I’ve downloaded the model and here it is.
Dodecahedron_Basic_Tutorial.skp (42.0 KB)

Sorry, on looking at your profile, I see you can’t use plugins as you are using the Web version which can’t run them. So I hope the alternative will help you.

You still need to draw carefully and accurately, being careful to get exact inferences at every stage.

A dodecahedron can also be drawn using a cube as a guide surprisingly easily. @jean_lemire_1 once posted a beautiful tutorial to an earlier incarnation of this forum.

A geodesic dome consists of different flat polygons arranged so as to approximate the surface of a sphere/hemisphere…
If you make the parts needed [as components] you can arrange these in 3d as needed…
There are many resources available… use Google… e.g.