This closed-loop cabled entrelac shape is based on the icosidodecahedron. The cables follow the edges of the Archimedean solid, but not all edges are used.
The goal with this shape was to keep 6 of the pentagons with the triangles that surround them. If this becomes a hat, I'm hoping that you'll be able to see the pentacle at the crown and 5 pentacles around the sides of the hat.
All of the triangles formed by the cables are the same size when knitted, perhaps stretched out a bit when the knitted piece is worn. We shall see.