What's going on with my boolean difference Modifier? Instructable

Hey All I am trying to recreate something I saw in an instructable a while back I can't figure out how to do it. They used Maya.

So I create the basic shape( the left one) and used the Boolean Modifier difference and the result is on the right. There is a sphere on the inside the design and the design is extruded inward.

How can I get this fixed? Thanks.
From an UV sphere, this can be done with 3 magic shortcuts:


AltP to poke the faces
AltJ to make quads from tris
AltE then individual faces to extrude faces




Additionally, it can be useful to keep these new vertices in a vertex group:



because it will allow to retrieve them easily for an eventual future modification. For instance: