[math-fun] Something special about 104

(Delurking for my first post.) A while back I saw a fact posted (on Pat's Blog, if anyone reads it) that said: 104 is the lowest known number of unit line segments that can exist in the plane, 4 touching at every vertex. I can find this repeated all over the internet, but nothing more about it. I read it as saying that the smallest 4-valent (quartic) unit distance graph has 104 vertices. Does that sound correct? Does anyone know where this might have come from? Thanks. I have enjoyed following the discussions on this list.