Straw Truncated Icosahedron Connector

A connector for making a truncated icosahedron out of straws.

The two sockets with flat bottoms are 108° from each other and form the outside of one of the solid's 12 pentagons. All pentagon edges are connected via one of these two sockets, while some hexagon edges are connected by the third socket. Also, any edge that originates in a third socket also terminates in a third socket.